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### 2016N729ij 15:3016:30C16:4517:45

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### 2016N85ij 16:0017:00

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### 2016N616i؁j 16:0017:00

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EGXg1 5K C-515 u
u
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Oa Newton polygons p-Qɂ
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### 2016N520ij 16:0017:00

㐔􉽃Z~i[Ƃ̋ÂłD

EGXg1 5K C-512 u
u
Y iIMIj
ʔzuƂ̑㐔wIɂ
Tv
ʔzuƂ̓xNgԒ̒ʂ̗LłB
ƂȒPȃP[X͎ʒ̗L̒łAɂ߂ăVvł邪Å􉽊wIΏۂɑ΂āA㐔E㐔􉽁Egݍ킹_E\_Eʑ􉽂ȂǗlXȃAv[p݂A͍gUłB
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### 2016N426i΁j 16:0017:15

EGXg1 5K C-513 u
u
Don Zagier iMax Planck Institute for Mathematicsj
Partitions and quasimodular forms: the Bloch-Okounkov theorem
Tv
The theorem of Bloch and Okounkov is a beautiful generalization of a theorem predicted some years ago by string theorists ("mirror symmetry in dimension one") and proved by Masanobu Kaneko and myself. I will explain the theorem and an extremely simple proof of it, and then discuss various generalizations found in joint work with Martin Moeller and their applications to the study of moduli spaces of flat surfaces.

### 2016N421i؁j 16:0017:00

EGXg1 5K C-515 u
u
Jennifer S. Balakrishnan iUniversity of Oxfordj
A database of elliptic curves ordered by height
Tv
Elliptic curves defined over the rational numbers are of great interest in modern number theory. The rank of an elliptic curve is a crucial invariant; indeed, there is a million-dollar prize problem about the rank!
There is great interest in the average rank of an elliptic curve. The minimalist conjecture is that the average rank should be 1/2. In 2007, Bektemirov-Mazur-Stein-Watkins, using well-known databases of elliptic curves, set out to numerically compute the average rank of elliptic curves, ordered by conductor. They found that "there is a somewhat more surprising interrelation between data and conjecture: they are not exactly in open conflict one with the other, but they are no great comfort to each other either."
The exciting recent work of Bhargava-Shankar has produced new theoretical upper bounds on average rank: when elliptic curves are ordered by height, the average rank is bounded above by 0.885. It was of interest to revisit the question of numerically computing average rank, under the ordering by height.
In joint work with Ho, Kaplan, Spicer, Stein, and Weigandt, we have assembled a new database of elliptic curves ordered by height. I will describe the database and some computations we have carried out.

### 2016N415ij 16:0017:00

EGXg1 5K C-512 u
u
^i吔j
ی^̔ʏf_ɂ锽~g̊V_
Tv
~HeckewWɂtwistی^L-֐̓lԂpiL-֐, Bertolini-Darmon-Prasanna, Brakocevic, Castella-Hsiehɂč\Ă. fpی^̒ʏf_̂Ƃ, Castella-HsiehɂlȂ, ΉSelmerQLł邱Ƃ, Heegner cycleEulernpĎĂ. ̍ułpʏf_̂ƂCastella-HsiehɑΉ錋ʂ.

### 2016N34ij 15:3016:30

EGXg1 5K C-512 u
u
c V i}gj
Ώ̋Ԃ̑GWɊ֘A㐔IΏ
Tv
LGrassmannl̂̋ɑGWƃRpNgLieQ̋ɑGQɊւčŋߓʂɂĉB
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ތʂ𒭂߂Ɗ{IȃRpNgLieQ̕\̕sόƊ֘A悤ɎvBɓc^IqƂ̋ŃRpNgLieQ̋ɑGQ𕪗ނAΉRpNgLie̎ȓ^Q̋ɑGQ̕ނ𓾂B ͂Lie݂̌ɉȑ΍Iȓ^̋ɑW̕ނɑΉĂB

### 2016N222ij 15:3016:30

EGXg1 5K C-512 u
u
isj
$GL(N)$̋ǏIی^U̐Kɂ
Tv
Langland ֎萫̓ʂȏꍇƂăGhXRs[IȎグ܂A͋Ǐ̏̏ꍇɂ͈ʂɒ萔{ĒĂ܂B̒萔{̕s萫邽߂ɃpPbg̓\̋Lqɂʂɕs萫܂B
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### 2016N219ij 14:3015:30C16:0017:00

EGXg1 5K C-512 u
u
Y ij
Colmez̏@IςpǏCvV^̍\ɂ
Tv
Bloch-̋ʉ͐\zAyсAV\z̗҂܂cȈʉƂāAa玁́ApiKA\̑SĂ̑iGaloisRzW[jɑ΂āAL֐̑㐔Iȉgł[[^݂iʉV\zjA[[^L֐Ɠl̊֐𖞂iCvV\zjƗ\zB{ũ^CgɂǏCvV^Ƃ́A[[^̊֐ɌǏqɂ̂ŁA[[^̋ǏłƂāASĂ̋ǏpiGalois\̑ɑ΂Ă݂̑\zĂiǏCvV\zjB
A@I(multiplicative convolution)Ƃ́AColmezɂGL_2(Q_p)ɑ΂piǏLanglandsΉɊւǍ̒ŁAǏpiGalois\ɕt(phi,Gamma)-Qɑ΂Ēꂽ鉉ZłB
{uł́ASĂ̋ǏpiGalois\̑ɑ΂āA@IςpǏCvV^̍\@ɂĂ̗\zB\zɂďؖłAyсA\zïꕔؖߒj玩RɓCvV^̖VȊ֌WɂĂB
u
Vi吔j
Hilbert eigenvariety̐d݂ł̌ŗLɂ
Tv
ŗLlĺieigenvarietyjƂ́A㐔Q̗LXΉߎŗLiHeckeŗLlnĵȂpi͓Il̂łBŗLll͔̂c̗LX΂̏ꍇɂ֕ƂċߔNdv𑝂Ă邪Å􉽓IȐ͂܂悭ĂȂBFpŕsȑ㐔̂ŁAp̏]S2ȉł̂ƂB{uł́AFHilbertی^ɑ΂Andreatta-Iovita-PillonǐŗLll̂ɂāA̐d݂ł̌ŗL̏ؖB

### 2016N122ij 16:0017:00

EGXg1 5K C-515 u
u
Denis Osipov iSteklov Institutej
Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields
Tv
I will describe the natural action of the discrete Heisenberg group that is the group of integer unipotent matrices of the third order, on the distribution space of a two-dimensional local field which appear from a flag on a two-dimensional arithmetic scheme. I calculate the traces of extended Heisenberg group in some irreducible subrepresentations of above representation as the classical Jacobi theta functions. The talk is based on joint paper with A.N. Parshin arXiv:1510.02423 [math.RT].

### 2016N18ij 15:3016:30C16:4517:45

EGXg1 5K C-512 u
u
i吔j
Distance to Cusps and Stability
Tv
In the study of totally real fields, Siegel introduced a distance from a modular point to a cusp and hence constructed corresponding fundamental domains. This distance was generalized to work for all number fields in Prof. Weng's study on non-abelian zeta functions. Motivated by this, working on product of rigid analytic upper half planes, we frist construct new distances between modular points and cusps. With the help of the correspondence between modular points and rank two bundles over curves defined over finite fields, we then obtain the following theorem.
Theorem: A rank two bundle on a curve over finite fields is Mumford semi-stable if and only if the distances of its associated modular point to all cusps are no less than one.
u
OY i吔j
Central extensions and reciprocity laws for arithmetic surfaces
Tv
OsipovParshin-BeilinsonAf[gĎ2̒Sg\A㐔IȖʂɑ΂Ă鑊ݖ@藧ƂĂB̗_K_2_㐔IȖʂɑ΂_Ƃ֘ABŁAZpIȖʁiinifinite partjɑ΂K_2_͋@\ĂȂ̂ŁAXArakelov_ɂƂÂSg̐Vȗ_𔭓WB̍ہAX͎ZpIȖʂɑ΂鑊ݖ@߂ɉX̎ZpIAf[gBĂ͎̌ZpIAf[_̈̉pƂĂ݂ȂB͉̌ѐ搶Ƃ̋łB

### 2015N1218ij 16:0017:00

EGXg1 5K C-515 u
u
O P iRj
On multiple polylogarithms in characteristic p
Tv
Let k be the rational function field over a finite field. We fix a finite place v and an infinite place of k. In this talk, we give a simultaneous vanishing principle for the v-adic Carlitz multiple polylogarithms (abbreviated as CMPLs) at algebraic points. This principle establishes the fact that the v-adic vanishing of CMPLs at algebraic points is equivalent to its infinite-adic counterpart being Eulerian. Here an infinite-adic convergence of a CMPL is called Eulerian if the ratio of this value over the w-th power of the fundamental period of the Carlitz module lies in k, where w is the weight of the CMPL. This reveals a nontrivial connection between the v-adic and infinite-adic worlds in positive characteristic. This is a joint work with Chieh-Yu Chang.

### 2015N1211ij 13:3014:30C14:4515:45C16:0017:00

3u܂DƎԁEꏊقȂ܂̂łӂD

EGXg1 5K C-502 u
u
Dohoon Choi iKorea Aerospace University/KIASj
Mock modular forms and modular traces of singular moduli
Tv
For a fundamental discriminant D<0, "singular moduli" means the value of a modular function at a CM point with discriminant D. Thanks to results of Zagier (for the case of level one), and Bruinier and Funke (for the case of general level), the generating function of modular traces of singular moduli for a fixed modular function is a mock forms of weight 3/2. For a fundamental discriminant D>0, Duke, Imamoglu, and Toth gave the definition of singular moduli of a modular function by using the integral of the modular function on a certain geodesic of a modular curve. They showed that modular traces of singular moduli (D>0) for a fixed modular function is a mock forms of weight 1/2.
Based on this progress on modular traces of singular moduli, in this talk I will talk about the following question: for a fixed modular function f, to find arithmetic connections between traces of singular moduli of f (d > 0) and those of f (d < 0) . To introduce our results with Subong Lim on this question, first I will review basic notations of mock modular forms and results on modularity of traces of singular moduli. Next, I will announce our results and then give a brief sketch of the proof of the results.
u
aO i吔j
Quantum modular forms and quantum invariants
Tv
A notion of quantum modular formsf was introduced by Zagier. A typical example is the Kontsevich-Zagier series, F(\tau)=\sum_{n >=0} \prod_{j=1}^n (1-q^j) I will talk about quantum modular forms from viewpoint of quantum invariants.
u
Youn-Seo Choi iKIASj
Ramanujan's mock theta functions in q-series
Tv
In this talk, I will introduce the results related to Ramanujan's (10th order) mock theta funtions and derived by employing the knowledge based on q-series.

### 2015N1030ij 16:0017:00

EGXg1 5K C-515 u
u
Gautami Bhowmik iUniversité de Lille 1j
Non vanishing of symmetric square L functions
Tv
The simultaneous non-vanishing of two automorphic L-functions has been studied in recent years both for their intrinsic interest and for their applications to other questions in number theory. We will present some known results and a few new developments on this question.

### 2015N1023ij 16:0017:00

u
icwj
@Q̒ς̃|Oɂ
Tv
|OƂ́ABeilinson-DeligneɂˉeR_i@QP_jɑ΂ď߂Ēꂽ_􉽓IȑΏۂŁǍ|O̍\́ABeilinson-LevinAWildeshausKingsȂǂɂAlXȌQXL[ɑ΂Ċg܂B̍uł́A@Q̒ςɑ΂|Ode Rham̋̓I\ƁǍʂ獡҂鐬ʂɂāA܂B

### 2015N1016ij 16:0017:00

u
H N iLۑwj
$Z_p$ꂽQ$p^n$_̂ȂQƓꌳ
Tv
{cɂQ̕ޗ_$Z_p$ꂽ1QɓKpƁCQ()^ɂȂ邱ƂƁCQ(Kꂽ)ꌳƁClɂȂ܂BŁCꌳƂ́CQ$p$@ƂҌFrobenius $p$掩ȏ^̌ŗLŁC$Z_p$W̑ɂȂ܂B
{uł́CQ$p^n$_̂ȂQ$G_{Q_p}$-QƂē^ł邱ƂƁCꌳ$p^n$@ƂēƁClł邱Ƃ܂Bؖ̌́CQ̓_ϊq(formal logarithm)̗_ƈv邱ƂłB

### 2015N95iyj 14:0015:00

̃Z~i[͊wʌ˂Ă܂D܂Cg|W[Z~i[Ƃ̋ÂłD ƗjEԁEꏊقȂ܂̂łӂD

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u
A iBwj
Arithmetic topology on branched covers of 3-manifolds
Tv
Arithmetic topology studies analogies and connections between number theory and 3-dimensional topology. In this talk, based on the analogies between primes and knots, number rings and 3-manifolds, we study analogues of idelic class field theory, genus theory, Iwasawa theory and Galois deformation theory in the context of 3-dimensional topology. We establish various foundational analogies in arithmetic topology.

### 2015N710ij 16:0017:00

u
V rY iLwj
Class field theory for open curves over local fields
Tv
In this talk, first we recall the class field theory for some arithmetic fields such as (higher dimensional) local fields, the function fields of one variable over a finite field. Then we introduce an analogue of such theory for an open (=non proper) curve over a local field. In particular, we decide the kernel and the cokernel of the reciprocity map.

### 2015N626ij 16:0017:00

u
TY iRIMSj
W 3 ̋З닖eŗL Cartier pf
Tv
ڒ́uЗ닖eŗLvƂ́AW̑㐔Ȑ̓KȐ𖞂ڑtˉêƂŁAiÓTIȁjp i Teichmuller _i̐W̕jɂ钆SIȊTOłB{uł́AW 3 ̏ꍇɁA̋З닖eŗLAyсA̓ʂȏꍇłuЗʏŗLv̒وqi= Hasse sϗʂ߂qj Cartier pfʂtɂẲsƎv܂B܂A̓tAp i Teichmuller _ɂ邠 2 ̊{̂ꂼےIAImI^邱Ƃł΂ƍlĂ܂B

### 2015N619ij 16:0017:00

g|W[Z~i[Ƃ̋ÂłD
u
O œl iBwj
On certain L-functions for deformations of knot group representations
Tv
We study the twisted knot module for the universal deformation of an SL(2)-representation of a knot group, and introduce an associated L-function, which may be seen as an analogue of algebraic p-adic L-function associated to the universal deformation of a Galois representation. We then verify affirmatively Mazur's problem on the order of a zero of the L-function by some concrete examples for 2-bridge knots.
This is the joint work with T. Kitayama, Y. Terashima and M. Morishita.

### 2015N612ij 16:0017:00

u
c iwj
K 2 WachQ̑̍\
Tv
̍uł́AK 2 WachQ̑ނ̓Iɍ\܂B\ɂ͒􉽑 p iIg܂B̑ Q_p 2\̕όԂɂĂ̐ȏ^܂B̑p 2NX^\̊Ҍ̌vZĂ܂B̍u̓e͎RƂ̋ɂ̂ł

### 2015N65ij 15:3016:30C16:4517:45

2u܂D

u
c 薡 i吔j
WǏ̂ APF gɕt閳x[XFWɂ
Tv
Langlands \zɂ Galois ́uvƑΉی^̑ƂāCux[XFWvƂ̂D㐔̂邢͍WǏ̗̂Lgɑ΂x[XFW GL(2) ɑ΂Ă LanglandsɂāCGL(n) ɑ΂Ă Arthur-Clozel ɂĂꂼ\ĂD̍uł͍WǏ̏̊S Z_p gɑ΂Ăx[XFW\ł邱ƂDKazhdan close fields ̗_ɂA͍WǏ̏GL(n) ̕ی^\𓙕WǏ̏ GL(n) ̕ی^\ֈڂƉ߂łD
u
Kimball Martin iUniversity of Oklahoma/swj
Arithmetic of L-values and the Jacquet-Langlands correspondence
Tv
Central L-values of elliptic curves encode much arithmetic information about these curves. Via the correspondence with modular forms, work of Waldspurger, Gross, and others further relates these L-values to arithmetic quadratic forms and quaternion algebras. In the first part of the talk, we will explicate some of these connections to draw interesting consequences with the aid of concrete examples. In the second part of the talk, we will discuss some conjectural generalizations to higher rank.

### 2015N515ij 15:3016:30C16:4517:45

2u܂D

u
R ^ iIMIj
qxgW[ɑ΂閾IȑΐՌ
Tv
RamakrishnanRogawski͐ȉ~_ɕtWی^L֐̒Sl̃xɊւ镽ς𖾎IɌvZBɔނ̌ʂFeigonWhitehouseɂĐHilbertW[̘gg݂ɊgꂽB܂AHilbert Maass̏ꍇɑΉގszɂė^ꂽBAĽʂɂ͉xsquare-freełƂ񂪉ۂĂB
{uł́AMaass̏ꍇ̓sžʂƐ̏ꍇFeigon-Whitehousěʂ̈ʂ̃x̏ꍇւ̊gɂĐB܂A
(1)SLl̔ŐA
(2)ʕ](subconvexity])A
(3)FourierẄlzA
(4)Hilbert_Heckê̊g原̑x̕]
(5)HilbertW[̏ꍇL֐̒Sl̕ς̖lɋLqł邱
Љ\łB̏ꍇ̌ʂ͓szj(qw)Ƃ̋łB
u
c iIMIj
ȉ~Ȑɂ˂_ƈҌ̊֌W
Tv
{uł́A㐔̏̑ȉ~Ȑɂ˂_̔񑶍ݐƈҌ^f_̊֌WɂčlB̓Iɂ́Aȉ~Ȑf_ňҌƂA˂_ȂƂʂЉBɁAf_ňҌȉ~Ȑ琶sg̗ЉB

### 2015N327ij 16:0017:00

u
R r i吔j
Periods of residual automorphic forms
Tv
ی^̂̒ĂQ̓KȕQ̐ϕ͎ƌĂ΂BL ̊֌W낢ȏꍇɊmFĂ邪A܂ł̖wǂ̌ł͐_Iی^݂̎̂lėB {uł́A_IłȂی^̎ɂċc_B_IłȂϕȕی^̓AC[V^C̗ƂēAIی^ƌĂ΂BĽQƂ̕QɂĎ0ɂȂȂIی^ނ: (GL(n+1)XGL(n),GL(n))A(GL(n,E),GL(n,F))A(GL(n)X^GL(n)X^GL(n),GL(n))BŁAEF̓񎟊gA^GL(n)GL(n)̓d핢ł.

### 2015N217i΁j 14:3015:30C16:0017:00

2u܂DƗjEԂقȂ܂̂łӂD

u
O iwj
LX[vی^ɕtKA\pi̐VȊ􉽓I\
Tv
W[ȐɕLZ_pQ̑w\ÃG^[RzW[Ƃđ傫ȃKA\\B𕁕ՃwbP̕LQƂėLX[ṽW[̑Ő؂邱ƂŃKA\pi𓾂B
u
R ֎m inwHwVXeHwȁj
Q̏̕ՕόԂɂ infinite ferns Ƃ̉pɂ
Tv
̍uł́AMazur ̗L̏ł̎@pāAQ̏̕ՕόԂ infinite ferns \BāẢpƂāAՕόԂŁA
Pjp-wild ȎwWŔPꂽ infinite fern Zariski ʑɊւfł邱
Qjp-supercuspidal ȓ_
ɂĊTB

### 2015N210i΁j 13:3014:30

ƗjEԁEꏊقȂ܂̂łӂD
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ˍN isw͌j
\Ǝ (,G^) Q
Tv
p i Hodge _̌ëƂāAK p i\̊iqf[^ŕނƂ̂܂B̎̐f[^Tong Liu ɂߔNꂽ(,G^) QłB semi-stable p i\̊iq𕪗ނ̂łAiBreuil Q́j]̐f[^ɑ΂Ab̂̐Εw Hodge-Tate d݂̐Ȃŕނł闝_łB(,G^) Q̒ɂ͂uZpIvȀO--(,G^) QƌĂт܂--ǂ\Ή̂Ƃ肪 Tong Liu ɂoĂ܂B̍uł͂̓ЉƎv܂B

### 2015N19ij 16:0017:00

u
Soma Purkait i吔j
Hecke algebras, new vectors and characterization of the new space
Tv
Let p be a prime. Let K_0(p^n) be the subgroup of GL_2(Z_p) consisting of matrices with lower left entry in p^n*Z_p. We shall consider the Hecke algebra of GL_2(Q_p) with respect to K_0(p^n) and its subalgebra that is supported on GL_2(Z_p) and describe them using generators and relations. This will allow us to explicitly describe the representations of GL_2(Z_p) having a K_0(p^n) fixed vector. We will translate this information to the classical setting that will lead us to give a criteria, only in terms of p, for a cusp form on Gamma_0(pM) to be in the new space.

### 2014N1219ij 16:0017:00

u
^ ikwwȁj
piGross-ZagierHeegner cyclepi
Tv
OłpiGross-ZagierƂ̉pɂĐ܂B 㔼ł͏dQȏ̔ʏf_ɂȉ~^ی^ piGross-ZagierɊւŋ߂̐iWɂďqׂ܂B ƂɌƂȂHeegner cyclepiԂɂĐ\łB

### 2014N1212ij 16:0017:30

􉽊wZ~i[E㐔􉽊wZ~i[Ƃ̋ÂłD ƏꏊEԂقȂ܂̂łӂD
ɓs} 3K Z~i[2
u
Iu iswwj
㐔l̂̃WCԂ́CGromov-Hausdorffɂ㐔􉽓IRpNg(K-moduli)ƃgsJ􉽓IRpNg
Tv
RpNg[}ʂ̃WCԂCDeligne-MumfordȐ̃WCƂăRpNg邱Ƃvg^CvƂāC̍̑㐔l̂̃WC_֊gƂb܂DϑlȊϓ_łƂ炦܂􉽓Iɂ́CoȌvʂ̊głP[[ACV^CvʂƂGromov-HausdorffƂ炦܂D ܂͋ߔNFanol̂Kahler-Einsteinvʂ̑ݖiK萫j̐iW𗘗pāCFanol̂̃WC(K-moduli)__܂ĎC蕡GȌۂ𐶂ރJrEibRj̏ꍇɘb]CɃA[xl̂̏ꍇɂďڂ܂D̏ꍇ̓P[[􉽂łȂC邱ƂŊ􉽓Iȃ~[Ώ̐̕(Strominger-Yau-Zaslow, Kontsevich-Soibelman, Gross-Siebert)ƗZCgsJ􉽊wi⌋wjƂ̐[֘A_Ԃ݂CWC̐VȃRpNg݂܂D

### 2014N1128ij 16:0017:00

u
Chandan Singh Dalawat iHarish-Chandra Research Institute/RIMSj
Some refined mass formulae
Tv
Serre had proved a beautiful mass formula involving all totally ramified extensions of a given degree over a local field (with finite residue field). We give various refinements of this formula in prime degree, computing the mass of various kinds of totally ramified extensions, for example those which are galoisian, or become galoisian over some given extension, etc. This is achieved by finding a canonical parametrisation of all separable extensions of prime degree, preserving the structures involved, including the ramification.

### 2014N1031ij 16:0017:00

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u
 Y ikCwٍZj
㐔X^bN̖̒Lx
Tv
㐔X^bN͑㐔l̂XL[̊TOʉ̂łAWČȂǂɗLpłB{uł̖͒Lx(ampleness)̊TODeligne-MumfordX^bN̏ꍇɊgBArtinX^bNւ̈ʉ݂̎ɂĂЉB

### 2014N1024ij 16:0017:00

u
r iHj
[[^̗_̍ŗאڊԊuzƂl
Tv
In this talk, we will present results on nearest neighbor spacing distributions for zeros of entire functions obtained by a sum of horizontal shifts of the Riemann xi-function. The first result is a description of the density functions of such nearest neighbor spacing distributions in terms of the M-function which is appeared in the theory of value distributions of the logarithmic derivative of the Riemann zeta-function on vertical lines. The second result is a limit behavior of the density function. These results are based on recent works of Y. Ihara and K. Matsumoto.

### 2014N102i؁j 16:0017:00

kbƂ̋ÂłD ƗjEꏊقȂ܂̂łӂD
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u
Mikhail Kapranov iKavli IPMUj
Relations between discriminants and resultants, their generalizations and categorification
Tv
The classical resultant $R(f,g)$ of two polynomials $f,g$ in one variable has many analogs in other areas of mathematics: the integral of product of first Chern classes, Legendre symbols, linking numbers and others. On the other hand, the classical discriminant $D(f)$ of a polynomial $f$ satisfies the coboundary" condition $R(f,g)^2 = D(fg)/(D(f) D(g))$. The talk will explain known and conjectural analogs of the discriminant and of the coboundary condition in other contexts where the analogs of the resultant make sense.

### 2014N829ij 14:3015:30

ƎԂقȂ܂̂łӂD
u
Ambrus Pal iImperial College Londonj
The p-adic monodromy group of abelian varieties over global function fields of characteristic p
Tv
We prove that the monodromy groups of the overconvergent crystalline Dieudonne modules of abelian varieties defied over global function fields are reductive, and after a finite base change they are the same as the monodromy groups of Galois representations on the corresponding l-adic Tate modules, for l different from p.

### 2014N81ij 16:0017:00

u
c O iUCLAj
Open problems on growth of Hecke fields
Tv
We discuss some open problems on how the field of rationality of automorphic representations grows over an analytic family (when level grows). Then we explain how other significant open problems follow from our conjectures. Finally out of examples/sketches of proven cases, we try to find a hopefully possible way of proving the conjectures.

### 2014N718ij 16:0017:00

u
q M i吔j
Ld[[^lƂ̎lłɂ
Tv
ʏ̑d[[^l̒Cef p ƂɁC p 钼Oőł؂ēLa mod p ̂W߂̂CuLd[[^lvƂΏۂW 0 ̑㐔̌ƂĒD ̗Ld[[^lʏ̑d[[^lƓlɖLȑΏۂłC܂ʏ̑d[[^l邢́urbNd[[^lvƖڂɊ֘AĂ邱Ƃ錋ʂ\zɂďqׂD iDon Zagier Ƃ̋j

### 2014N52ij 16:0017:00

u
Don Blasius iUCLAj
Shimura varieties and complex conjugation
Tv
Work of Shimura, Langlands, Milne-Shih, and, more recently, Taylor have examined the action of complex conjugation on Shimura varieties. We study this topic from the viewpoint of the general theory of these varieties, with the goal of establishing, in all applicable cases where the canonical field of definition E is complex, descents of the system of varieties to the maximal totally real subfield E^+ of E. We also study the reciprocity law for the connected components of the variety, and the reciprocity law at the CM points. We plan to conclude by mentioning the problem of integral models, and zeta functions, of these descended systems. The work is joint with Lucio Guerberoff (UCLA) and remains in progress.

### 2014N425ij 16:0017:00

u
Dohoon Choi iKorea aerospace universityj
Congruences for weakly holomorphic modular forms
Tv
In this talk, I will talk about special congruences for weakly holomorphic modular forms. Weakly holomorphic modular forms mean that they are modular forms but can have poles at some cusps. These modular forms have played important roles as generating functions for several objects such as the partition function, traces of singular moduli and so on. This talk will discuss on special congruences concerning with weakly holomorphic modular forms, which are motivated from congruences for the partition function studied by Ramanujan.

### 2014N418ij 16:0017:00

g|W[Z~i[Ƃ̍łDƏꏊقȂ܂̂łӂD

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u
V mj iBwj
Idèlic Class Field Theory for 3-manifolds
Tv
ޑ̘_Ƃ͑㐔̂̃A[xĝLq闝_łBCf[͗ޑ̘_\ۂC. Chevalleyɂ蓱ꂽB{uł́A3g|W[Ɛ_̗ގɏ]A3l̂ɂCf[QACf[ތQ𓱓A3l̂ɂǏޑ̘_Aޑ̘_̗ގЉB

### 2013N1122ij 16:0017:00

u
Ñ isww@ Hwȁj
d[[^֐̓ٓ_pidL֐̍\iÏpaAXA{k񎁂Ƃ̋j
Tv
ʂEuler-Zagier^̑d[[^֐͑ singularity , SĂ entire Ȋ֐\鎩RȎ@Љ. , ̂悤ɂĂł֐, {̑d[[^֐̗L̘aƂĂ킷Ƃł. ̉ߒŌ entire Ȋ֐́i̐_ł́jpiԂƂ, pidL֐\. Kubota-Leopoldt piL֐̑dƂ݂邪, ̐_ł̒lpid|OpĂ킳. ܂pƂ, Bernoulli̖KummeȓdȂǂ.

### 2013N719ij 16:0017:00

u
Sinnou David ip6wwwȁj
Points of small height on abelian varieties over function fields
Tv
An old conjecture of Lang (for elliptic curves) generalized by Silverman, asserts that the Néron-Tate height of a rational point of an abelian variety defined over a number field can be bounded below linearly in terms of the Faltings height of the underlying abelian variety. We shall explore the function field analogue of this problem.

### 2013N426ij 16:3017:20

wAutomorphic Functions and Arithmetic GeometryxƂ̍łDƎԂقȂ܂̂łӂD

u
ɓ Nj iswj
Endoscopic decomposition of the cohomology of the Rapoport-Zink space for GU(3)
Tv
It is widely believed that the l-adic cohomology of Rapoport-Zink spaces realize the local Langlands and Jacquet-Langlands correspondences. For the Lubin-Tate spaces or Drinfeld upper half spaces, it was established by Harris-Taylor and Boyer. It turns out that supercuspidal representations of GL(n) appears only in the middle degree cohomology. However, this is not true for more general Rapoport-Zink spaces. In this talk, we consider supercuspidal representations in the cohomology of the Rapoport-Zink space for GU(3). A new phenomenon is that certain supercuspidal representations, which are related to non-tempered endoscopy, appear outside the middle degree. Similar results can be obtained for GSp(4) assuming some form of Arthur's conjecture. This is a joint work with Yoichi Mieda.

### 2013N220ij 16:0017:00

ƗjقȂ܂̂łӂD

u
Ԓ L i吔j
IC[ςтfBN̋ɂ
Tv
{uł́A[}[[^֐̃IC[ς̗ՊËɂ鋓ƁA fzA_z̊֌WɊւ錋ʂЉB ܂A[}[[^֐̋t̓rEX֐pfBN\ Aɋ߂fBN̐ΎOɂc_B ܂AIC[ς̋ƃfBN̎Ɋւ鐔lvZЉB

### 2013N28ij 16:0017:00

u
gc i吔j
􉽓Iʑ
Tv
􉽕̍ʑ͑OXI̐włA܂łǂWĂāAɂȂĂ邩B

### 2013N111ij 16:0017:00

u
] F iswj
TώxNgԂ Z_p Oɂ
Tv
TώxNgԂpi̋O肷邱Ƃ͋Ǐ[[^֐̌vZ]Ƃϓ_dvł. ɂĕsώ_IȃAv[lC̗ɂĉ.

### 2012N1214ij 16:0017:00

u
iswj
Endoscopy for covering groups of SL_2
Tv
This is a joint work with T. Ikeda.
Although covering groups are not algebraic group, phoenomena analogous to the endoscopy had been found for the covering groups. In this talk, I will explain endoscopies for covering groups of SL_2. For some cases we succeeded to construct covering groups of quaternion algebra. In this talk, I will also explain the functoriality for such covering groups of inner forms of SL_2 and GL_2.

### 2012N1130ij 16:0017:00

u
Wen-Ching Winnie Li iThe Pennsylvania State University/Tsinghua Universityj
Zeta functions in combinatorics and number theory
Tv
Roughly speaking, a zeta function is a counting function. Well-known zeta functions in number theory include the Riemann zeta function, the zeta function attached to an algebraic variety defined over a finite field, and Selberg zeta functions. They count integral ideals of a given norm, the number of solutions over a finite field, and the equivalence classes of tailless geodesics in a compact Riemann surface, respectively. A combinatorial zeta function counts tailless geodesic cycles of a given length in a finite simplicial complex. One-dimensional complexes are graphs; attached to graphs are the well-studied Ihara zeta functions. Zeta functions attached to 2-dimensional complexes are recently obtained in joint work with Ming-Hsuan Kang, Yang Fang and Chian-Jen Wang by considering finite quotients of the Bruhat-Tits buildings associated to SL(3) and Sp(4) over a p-adic field.
The purpose of this talk is to show connections between combinatorics and number theory, using zeta functions as a theme. We shall give closed form expressions of the combinatorial zeta functions mentioned above, and compare their features with those of the zeta functions for varieties over finite fields.

### 2012N112ij 16:0017:00

u
iswj
Compactifying Spec Z
Tv
Tvipj
The main goal of this talk is to introduce a suitable category in which the standard compactification of the Zariski spectrum of rational integers can be characterized as the universal compactification of Spec Z, which is analogous to the so-called Zariski-Riemann space in algebraic geometry. For this aim, we need to introduce a new algebraic type, to which we refer as convexoids". Also, some technical generalizations of the scheme theory are required. These setups are time consuming, but it deserves attention, since many ad-hoc definitions in arithmetics can be justified as the correct analogy of those in algebraic geometry.

### 2012N1019ij 16:1017:00

wSymposium on ARITHMETIC GEOMETRYxƂ̍łDƎԂقȂ܂̂łӂD

u
Dennis Osipov iSteklov Mathematical Institutej
Two-dimensional harmonic analysis and the Riemann-Roch theorem for algebraic surfaces over finite fields
Tv
This is a survey talk on joint papers with A.N. Parshin about how to construct the main ingredients of harmonic analysis for adelic rings of two-dimensional arithmetic schemes (the main difficulty is that this adelic ring is not locally compact). The application of the theory is a new proof of the Riemann-Roch theorem for algebraic surfaces over finite fields, using the analogs of Poisson formulas like the well-known proof for algebraic curves by means of usual harmonic analysis. The references are arXiv:0707.1766v3 [math.AG], arXiv:0912.1577v2 [math.AG] and arXiv:1107.0408v2 [math.AG].

### 2012N713ij 16:0017:00

u
iwj
KQ̃VvNeBbNQɊւ郆j|egOϕ̌W ɂāiOn coefficients of unipotent orbital integrals for the symplectic group of rank 2j
Tv
̌Werner HoffmannƂ̋łBA[T[Ռ̊􉽃TCh͏dݕtOϕ̐^ŕ\B̓WJɂ郆j|egOϕ̌W͈̐ʓIɕĂȂB܂GL(2), SL(2), GL(3), SL(3)̏ꍇɊւWɂĂ̊m̌ʂ𕜏KB̏ꍇ̌W̓ffLg[[^֐s=1ɂ郍[WJ̒萔wbPL֐s=1̓lȂǂɂċLqBɊKQ̃VvNeBbNQ̃j|egOϕ̌WɊւX̎匋ʂɂďqׂB̏ꍇɂ̓ffLg[[^֐ƃwbPL֐ɉĂQQ̋ԂɊւVJ[[^֐s=3/2ɂ郍[WJ̒萔ɂČW\邱ƂBɁǍʂƈ艻Ƃ̊֌WɂĂB
Tvipj
This is a joint work with Werner Hoffmann. The geometric side of the Arthur trace formula is expressed as a linear combination of weighted orbital integrals. In the expansion, coefficients of unipotent orbital integrals are not understood in general. First, we review some known results on coefficients for GL(2), SL(2), GL(3), and SL(3). In such the cases, the coefficients are expressed by the constant term of the Laurent expansion of the Dedekind zeta function at s=1, the special values of the Hecke L-functions at s=1, and so on. Next, we mention our main result on coefficients of unipotent orbital integrals for the symplectic group of rank 2. We show that the coefficients are expressed by the constant term of the Laurent expansion of the Shintani zeta function for the space of binary quadratic forms at s=3/2 in addition to the Dedekind zeta function and the Hecke L-functions. Furthermore, we explain relations between these results and stabilization.

### 2012N629ij 16:0017:00

u
Y i吔j
Higgs crystals and Galois cohomology
Tv
A p-adic analogue of Simpson correspondence between Higgs bundles and representations of fundamental groups was given by G. Faltings around ten years ago. His theory, however, depends on the choice of a certain infinitesimal deformation of a variety, which may not exist in general. This problem can be resolved by working with a kind of crystals, which I call "Higgs crystals", instead of bundles. With this point of view, one can also naturally construct a "Higgs analogue" of the p-adic period ring Acrys, and study the Galois cohomology of the representation associated to a Higgs crystal. I will first give an introduction of the work of Faltings, and then talk on the results above.

### 2012N61ij 16:3017:20

uSymposium on Arithmetic and GeometryvƂ̍łDƎԂقȂ܂̂łӂD

u
iF{wj
On the moduli space of pure one-dimensional sheaves with c_1=5 and chi=0 on P^2
Tv
Le Potier's strange duality conjecture for sheaves on P^2 motivates us to compute the holomorphic Euler characteristic of a line bundle on the moduli space of semistable pure one-dimensional sheaves on P^2. In this talk we study the structure of the moduli space of semistable pure one-dimensional sheaves with c_1=5 and chi=0 on P^2, especially the locus consisting of sheaves with non-vanishing cohomology.

### 2012N521ij 16:0017:00

g|W[Z~i[Ƃ̍łDƗjقȂ܂̂łӂD

u
L q iFlorida State University/wj
Mapping classes associated to mixed-sign Coxeter systems
Tv
The smallest known accumulation point of the genus-normalized dilatations of closed oriented surfaces is L = 1 + golden mean. In this talk we show how to construct a mapping class on an oriented surface from an ordered simply-laced Coxeter fat graph. We show that minimum dilatation orientable pseudo-Anosov mapping classes for small genus can be constructed using this method. We also find a sequence of mapping classes with unbounded genus, whose genus-normalized dilatations converge to L. @@@

### 2012N511ij 16:0017:00

u
R r i吔j
e[^ΉƕWL֐iTheta correspondence and standard L-functionsj
Tv
ʐ^Q̊_I\̕WL֐͑SʂŐłBAVvNeBbNQⒼQ̊_I\̕WL֐͈ʂɐł͂ȂB {uł́A̋ɂe[^Ή̗_ƌтĉ߂BɒQ̏ꍇɁAɂłȂle[^Ή݂̑Ɗ֌Wt邱ƂbB
Tvipj
The standard L-functions of irreducible cuspidal automorphic representations of general linear groups are holomorphic everywhere on the whole complex plane. But, standard L-functions of irreducible cuspidal automorphic representations of symplectic or orthogonal groups are not entire in general. In this talk, I give an interpretation of the poles of the standard L-functions in terms of theory of theta liftings. Moreover, in the case of orthogonal groups, I relate the existence of theta liftings to not only poles but also special values of the standard L-functions.

### 2012N58i΁j 16:0017:00

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u
Don Zagier iMax-Planck Institut/College de Francej
Multiple zeta values, Feynman diagrams, mixed Tate motives, and mod p multiple zeta values

### 2012N413ij 16:0017:00

u
Alan Lauder iUniversity of Oxfordj
Explicit rational points on elliptic curves
Tv
I will describe an efficient algorithm for computing special values of certain p-adic L-functions, and discuss an application to the explicit construction of rational points on elliptic curves.

### 2012N217ij 16:0017:00

u
rc i嗝wȁj
Hilbert modular form Ɋւ Kohnen plus Ԃɂ
Tv
d k+(1/2) ̈ϐی^̋ $S_{k+(1/2)}(\Gamma_0(4))$ ɑ΂āAKohnen plus space ƌ镔 $S_{k+(1/2)}^+(\Gamma(0))$ A$S_{2k}(SL_2(\mathbb{Z}))$ Hecke QƂē^ɂȂ邱ƂmĂB̗_ʂ̑㐔̏ Hilbert ی^ɑ΂Ċg邱ƂڕWɂB @@@
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Tvipj
There exists a subspace $S_{k+(1/2)}^+(\Gamma(0))$ of the space $S_{k+(1/2)}(\Gamma_0(4))$ of modular forms of weight $k+(1/2)$. It is known that $S_{k+(1/2)}^+(\Gamma(0))$ is isomorphic to $S_{2k}(SL_2(\mathbb{Z}))$ as a Hecke module. We consider an generalization of this theory to Hilbert modular forms over a totally real field.

### 2012N113ij 16:0017:00

u
l-adic representations of etale fundamental groups of curves (joint work with Akio Tamagawa)
Tv
The aim of this talk is to present an overview of my joint work with Akio Tamagawa (R.I.M.S., Kyoto University) on l-adic representations of etale fundamental groups of curves.

### 2011N1222i؁j 16:0017:00

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u
͑ ikCwj
On the Duke-Imamoglu lifting of p-adic families of elliptic modular forms and its applications
Tv
As a generalization of the Saito-Kurokawa lifting to the higher genus, Ikeda constructed a Langlands functorial lifting of elliptic modular forms to Siegel modular forms (i.e. automorphic forms on the symplectic group) of arbitrary even genus, which is so-called the Duke-Imamoglu (or Ikeda) lifting. On the other hand, Hida and Coleman constructed the $p$-adic families of elliptic modular forms of finite slope, varying continuously $p$-adically the weight and the Nebentypus characters, which could be interpolated by some g$\Lambda$-adich modular forms. In this context, starting from the $p$-adic families of elliptic modular forms, we'd show you how to construct certain p-adic families of Siegel modular forms of even genus by means of an analogy of Ikeda's lifting process. Moreover, as an application, we'd also like to propose a generalized Duke-Imamoglu lifting to be adaptable to some elliptic modular forms of $p$-power level, and also to some automorphic representations of PGL(2) over any totally real field.

### 2011N1216ij 16:0017:00

g|W[Z~i[Ƃ̍łD

u
A i吔j
3l̂̕핢̃zW[ɂāiOn the homology of branched coverings of 3-manifoldsj
Tv
_Ig|W[ɂ3l̂Ɛ̗ގɏ]C3l̂̕핢̃zW[ɂčl@ʂ񍐂D ɁCCfAތQCPQɊւV̒藝CHilbert̒藝90̗_^̒藝3g|W[ɂގD܂C핢 2-TCNWGaloisRzW[ʑsϗʂł邱ƂC2-TCNQƒPQ̗ގɂĐVȓ@^D
Tvipj
Following the analogies between 3-manifolds and number rings in arithmetic topology, we study the homology of branched covers of 3-manifolds. In particular, we show some analogues of Iwasawa's theorems on ideal class groups and unit groups, Hilbert's Satz 90, and some genus theory type results in the context of 3-dimensional topology. We also prove that the 2-cycles valued Galois cohomology of branched covers is a topological invariant, and give a new insight into the analogy between 2-cycle groups and unit groups.

### 2011N114ij 16:0017:00

u
sz v ikwj
ʒ􉽊֐ϕɎ_IJrEEl̑ɂāiArithmetic families of Calabi-Yau varieties with certain generalized hypergeometric functions as periodsj
Tv
ʒ􉽊֐${}_{n+1}F_n(1/2, \cdots, 1/2; 1, \cdots, 1; \lambda)$ϕɂ$\lambda$ Ȑ$\mathbb P_{\mathbb Z[1/2]}^1 \setminus \{0, 1, \infty\}$̃JrEEl̑̍\ÃRzW[(xbAhA$\ell$ iG^[ANX^)肷BɁAtKA\̕ی^Ȃǂ̐_IpɂĐGB(R玁Ƃ̋)
Tvipj
We construct a family of Calabi-Yau varieties over a $\lambda$-line $\mathbb P_{\mathbb Z[1/2]}^1 \setminus \{0, 1, \infty\}$ with a certain generalized hypergeometric function as a period and determine its cohomolgies (Betti, de Rham, $\ell$-adic etale, crystalline). We also mention modularity of attached Galois representations. (Joint work with Takuya Yamauchi)

### 2011N1021ij 15:3016:30C16:4517:45

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u
{J a i吔j
xNX^RzW[̗LiFiniteness of Crystalline Cohomology of Higher Levelj
Tv
xNX^RzW[́C1990 N Berthelot ɂ蓱ꂽRzW[łCNX^RzW[Εw DVR ̃XL[ɑ΂Ăł悤ǂ̂łDƂ낪CxNX^RzW[ɂ|AJ͕̕GłC䂦 ̃RzW[́Cg[W𖳎舵ƂD{uł́C̍xNX^RzW[̗L̏ؖЉD
Tvipj
The crystalline cohomology of higher level is a generalization of the classical crystalline cohomology to ramified base DVRs, which was introduced by Berthelot around 1990. The crystalline Poincare lemma for this cohomology is however very complicated, and it is difficult to treat the integral structure of the cohomology. In this talk, we see how to prove the finiteness and other fundamental properties of this cohomology in spite of the complexity.
u
O} m i吔j
PEL ^Jul̂̃RpNgRzW[Ɨאڗ֑̃RzW[iCompactly supported cohomology and nearby cycle cohomology of open Shimura varieties of PEL typej
Tv
ul̂ l iRzW[͐_ѐ_I㐔􉽂ɂďdvȌe[}łD̍uł́Cul̂ PEL ^łꍇCȂ킿̍\tA[xl̂̃WCԂƂēꍇɁC̃RpNgRzW[i邢͌Rz W[ł悢jƗאڗ֑̃RzW[̔rsDul̂RpNgłꍇɂ͂ 2 ̃RzW[͓^ɂȂ邪CRpNgłȂꍇ͓^Ƃ͌ȂDł́Cul̂RpNgłȂꍇlĈƂɂ 2 ̃RzW[̒_͓^łƂʂD܂C̒藝̉pЉ\łDȂC{͍䒼BƂ̋ łD
Tvipj
The l-adic cohomology of Shimura varieties are very important in number theory and arithmetic algebraic geometry. In this talk, I compare the compactly supported cohomology (or the intersection cohomology) and the nearby cycle cohomology of a Shimura variety of PEL type, namely, the moduli space of abelian varieties with several additional structures. Needless to say, they are isomorphic if a Shimura variety is proper. I will consider the case where a Shimura variety is not proper, and prove that the supercuspidal part of these two cohomology groups are the same. We will also give some applications of this theorem. This is a joint work with Naoki Imai.

### 2011N1014ij 16:0017:30

͊wnZ~i[Ƃ̍łDƈقȂ90uł̂łӂD

u
R T isH|@ۑwj
A quantitative equidistribution in dynamics over ultrametric fields and complex numbers
Tv
{uł͔ALfXI͊wnѕf͊wnɂ铙z藝̌덷] Vgg݂sƂɁApƂĐ̂є̏̐_͊wn̏ꍇڏqB

### 2011N822ij 16:0017:00

ƗjقȂ܂̂łӂD

u
Ambrus Pal iImperial College Londonj
Bounds on the ranks of Mordell-Weil groups of abelian varieties over extensions of function fields
Tv
We prove a new upper bound on the ranks of Mordell-Weil groups of abelian varieties over function fields after regular geometrically Galois extensions of the base field which applies to fields of arbitrary characteristic, improving on previous results of Silverman, Ellenberg and Pacheco. We use Hodge theory to prove an even stronger bound for elliptic curves when the base field has characteristic zero.

### 2011N817ij 16:0017:00

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u
Andrew Booker iBristol Universityj
Some remarks on the GL(2) converse theorem
Tv
I will discuss some ways of weakening the hypotheses of the GL(2) converse theorem over number fields. In particular, I will describe a version of Weil's classical converse theorem that allows for essentially arbitrary poles for almost all twists. If time permits, I will mention an application to Saito-Kurokawa lifts.

### 2011N722ij 16:0017:30

ƈقȂ90uł̂łӂD

u
c O iUCLAj
Big Galois representations and p-adic L-functions
Tv
Let $p\ge5$ be a prime. If an irreducible component of the spectrum of the ebigf ordinary Hecke algebra does not have complex multiplication, under mild assumptions, we prove that the image of its Galois representation contains, up to finite error, a principal congruence subgroup $\Gamma(L)$ of $SL_2(\mathbb{Z}_p[[T]])$ for a principal ideal $(L)\ne0$ of $\mathbb{Z}_p[[T]]$ for the canonical gweighth variable $T$. If nontrivial (i.e., $L\ne1$), the power series $L$ is proven to be a factor of the Kubota-Leopoldt $p$-adic $L$-function or of the square of the anticyclotomic Katz $p$-adic $L$-function (or a power of of $(1+T)^{p^m}-1)$).

### 2011N715ij 16:0017:00

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### 2011N520ij 15:3016:30C16:4517:45

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Is ikCwn@\j
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Barthel-LivnéCpȉGL(2)̖@p\ɑ΂Ēٕ\̊TOC񒴓ٕ\̕ނs DHerzigɂCٕ\͈̒ʂ̕^piȖQɊgCHerziǵCGL(n)̏ꍇɊ񋖗e@p\̕ނ eٕ\̕ނւƋADɁC񋖗e@p\قł邱Ƃƒ_ł邱Ƃ̓l]D̒藝̕^piȖQւ ʉЉD
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iF{wj
On lattices in $\mathrm{PGL}_3(\mathbf{Q}_2)$ (joint-work with Daniel Allcock)
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A tree-theoretic approach to classify lattices in $\mathrm{PGL}_2$ of $p$-adic fields, developed in my past works, partly by collaboration with G. Cornelissen and A. Kontogeorgis, gave an effective way to describe lattices in this $p$-adic Lie group, and was applied to numerous problems in geometry of algebraic curves. Daniel Allcock and I tried to carry out the similar story for $\mathrm{PGL}_3$. What we obtained so far are the following results, which I am going to speak about: $\mathrm{PGL}_3(\mathbf{Q}_2)$ has exactly two lattices of minimal covolume, which are both arithmetic, commensurable to each other; moreover, one of these two lattices is the one constructed by Mumford in his famous construction of a fake projective plane.

### 2011N422ij 15:1516:15C16:3017:30

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Haseo Ki iYonsei Universityj
On the zeros of Weng zeta functions for Chevalley groups (a collaboration with Komori and Suzuki)
Tv
We prove that all but finitely many zeros of Weng's zeta function for a Chevalley group defined over the field of rationals are simple and on the critical line.
u
R iLcj
GL(n)ł̕ی^グƐpizba_
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܂ABerger-Li-ZhuɂGL(2)łWachQ̖̍\nɊgB̍\WachQ̃ WCpKisin̎@ɂǏ̂̕Օό̐搫𓱂BTaylorƂ͎̋҂ɂAGL(n)̏ꍇ̕ی^ Ƃ̐ݓIی^ɂpf_ł̏ɂ߂ƂpB̌͋sẅc厁Ƃ̋łB

### 2011N415ij 15:3016:30, 16:4517:45

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Ó MO i吔j
Elementary Computation of the stable reduction of the Lubin-Tate space $\mathcal{X}(\pi^2)$
Tv
Lubin-Tate$\mathcal{X}(\pi^n)$́AL̂̑㐔̃j[NȌQ Drinfeld\t̕όԂɂȂĂBQ̍2̏ꍇɂ́A̋Ԃrigid analyticȈӖŋȐɂȂĂB̏ꍇLubin-TateԂ̈胂fAƂlB̖ɊւāA ߁AJ. Weinstein͑gDIɁix𑖂点ājLubin-Tatë胂fvZ@oĂB
Coleman-McmurdỹW[Ȑ$X_0(p^3)$̈胂f̌vZɊÂIȕ@Ńx2̏ꍇLubin-TateԂ̈胂f̓IɌ肵̂łɂĂ̌ʂЉB
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Ԓ L i吔j
}[[xC̈ʉƒ􉽊֐
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fW̑ϐ[ɑ΂C̃}[[x̓[̐Βl̑ΐCPʉ~̒Ϗ Őϕ邱ƂŒDϐ̏ꍇ, ̃}[[x̗͑_pĕ\ƂłDCϐꍇCʂɊȒPȌ邱Ƃ͊҂łȂC̓Iȑɑ΂C }[[x[[^֐̓lȂǂpĕ\mĂD
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### 2011N216ij 16:0017:00

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ʐ Rj i吔j
㐔̏̃A[xl̂Ɋւ邠L\zɂāiChristopher Rasmussen Ƃ̋j
Tv
L㐔 K Ɣ񕉐 g ^ꂽAK g A[xl A ̓^ނƑf l ̑głāAA ɕt K l iKA\ l ̊OŕsŁA K(_l) ɐƑ l ɂȂ悤Ȃ̂͗LȂƂARasmussen Ɨ\zċi߂Ă܂B
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### 2011N24ij 16:0017:00

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Xavier Dahan i吔j
Ramanujan graphs of very large girth based on octonions iJ.-P. TillichƂ̋CarXiv:1011.2642j
Tv
This work presents a construction of some families of regular graphs that have two aspects:
1. 1) they are "Ramanujan", which means that their adjacency matrices have small eigenvalues, besides the largest one(s).
2. 2) they have a large "girth" (there is no short walk that permits to come back to the starting vertex of the walk).
Point 1) implies that they are good "expander graphs": these graphs have numerous applications in Computer & Information science, and more recently in "pure" mathematics as well (Cf. [2,3]). Point 2) is related to a very classical upper bound in graph theory, the "Moore bound". It follows from an elementary counting argument, but it is not known how tight is this bound. The large girth graphs constructed here, show that the Moore bound is not too bad. We follow the strategy of the landmark paper [1], but use octonions instead of quaternions. In the talk, we will review the basic concepts of spectral graph theory and expanders, then focus on the more mathematical aspects of this work. (Ramanujan conjecture and elementary arithmetic of octonions)
1. [1] Ramanujan graphs. Lubotzky-Philips-Sarnak, Combinatorica, 1988.
2. [2] Expander graphs and their applications. Linial, Hoory, Wigderson, Bull. of the AMS, 2006.
3. [3] Video lecture of Avi Wigderson (IAS, Princeton) for an overview of expanders

### 2011N128ij 15:3016:30, 16:4517:45

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1939NAL. Redei͗L̏̂82ʑ̊gɂf̕@LqgvL𓱓BXÍAіڂƑf̗ގ̎_A RedeĩgvL3d܂萔iMilnorsϗʁjƂĉ߂Aʂndׂ]ĹA2^N iN=n(n-1)/2jHeisenberggɂĎׂł邱ƂNB̍uł́A64Heisenbergg ̓Iȍ\^A4dׂ]L𓱓BɁAX4dׂ]LX4dMilnorsϗʂɈv邱ƁAȂ킿A4d܂ 萔̐_Iގł邱ƂB

### 2011N114ij 16:0017:00

u
Cristian Virdol i吔j
Potential modularity for l-adic representations and applications
Tv
I will describe the simultaneous potential modularity of a finite number of elliptic curves defined over an arbitrary totally real number field. As a consequence I will prove some results on Birch and Swinnerton-Dyer conjecture for elliptic curves defined over totally real fields, and also on Tate conjecture for a product of two or four elliptic curves defined over totally real fields.

### 2010N1129ij 16:0017:00

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c O iUCLAj
Hecke fields and L-invariant
Tv
Take a p-adic analytic family of Hecke eigenforms f_P with slope 0 (for an odd prime). Then we prove that Q(a(p,f_P)|P) is a finite extension of the cyclotomic field of all p-power roots of unity if and only if the family has complex multiplication. As a corollary of this, the L-invariant of the adjoint square L is constant on the family if and only if the family has complex multiplication.

### 2010N1126ij 15:0016:00

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ms i吔j
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_IDQƂ90NBerthelotɂēꂽRzW[_ŁCDQ̗_̕Wp̗̑̏ގ̗ _łD{uł͐_IDQЉCTCN𒆐SɎ̌ʂɂĘbƎvDy_IDQ̗_ЉƁC܂TC NsϗʂSwanƖڂɊւĂƂ̌ʂЉD͓TCN̏\Ă邱ƂĂ DɓTCNڂׂ邽߂ɓǏwЉC{IȐɂĘbDŌɂ̉pƍ̖ڕWɊ֘AāCp i̋ǏFourierϊɂĘbƎvĂD

### 2010N1125i؁j 15:3016:30

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WCԂȂǂ\Ƃ萫ƂTO΂ΏdvƂȂB萫͎_ɂĂ܂܂ȂƂ炦ł, Lȗ_\zĂB{uł́C̊TO㐔X^bN̎_璭߁CʂArtinX^bNɈ_̊TO𓱓B̈萫͕W ɂẮCArtinX^bNaWCԂ߂̕ՓIȏB @͂߂Ă̈萫Ɗ֌Ŵ鎖FGITiMumford̊􉽊wIsώ_jCKeel-Mori̒藝CX^bN̋Ǐ\CzIȃR pNgɐGB

### 2010N1112ij 16:0017:00

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Lc l iwoϊwj
Elliptic curves with isomorphic 3-torsion structure
Tv
EL̏ꂽȉ~ȐƂBÊR_̂ȂQE[3]ɂ̓KAQRɍpAKAQ̍\A ł͂̃KAQ^ł悤ȑȉ~Ȑ̑{F_t}\ƂlBF_t[3]E[3]̊Ԃ̓^ʑWeilyA OɊւēʑɂȂꍇƔʑɂȂꍇ̂Q̏ꍇ邪AǂɂĂʋȐ̂փVAɊÂÓTIȊ􉽊wpč\ B

### 2010N1029ij 16:0017:00

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Federico Pellarin iUniversité de Saint-Etiennej
Deformations and families of Drinfeld quasi-modular forms
Tv
The so-called Drinfeld quasi-modular forms are natural analogues of classical quasi-modular forms, over function fields of positive characteristic. In this talk we will introduce a class of deformations of Drinfeld quasi-modular forms which have themselves certain automorphic properties. As an application of the theory of these deformations, we will describe some families of "extremal" Drinfeld quasi-modular forms and make some prediction on their general structure.

### 2010N910ij 14:3015:30C16:0017:00

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WƍW̗LRQXL[̕ΉiRamification correspondence of finite flat group schemes of equal and mixed characteristicsj
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Let K be a complete discrete valuation field of mixed characteritic (0,p) with perfect residue field k. It is well-known that we have an equivalence of categories between the category of finite flat group schemes over O_K killed by p and a category of finite flat group schemes over k[[u]] killed by their Verschiebungs which induces the field-of-norm functor on the generic fiber. In this talk, we show that the ramification subgroups of two corresponding finite flat group schemes of equal and mixed characteristics via this equivalence are isomorphic to each other.
u
Kim Wansu iImperial College, Londonj
The classification of p-divisible groups over p-adic discrete valuation rings
Tv
Let O_K be a p-adic discrete valuation ring with perfect residue field k. We classify p-divisible groups and p-power order finite flat group schemes over O_K in terms of certain Frobenius modules over S:=W(k)[[u]]. We also show the compatibility with crystalline Dieudonné theory and Tate module functor (as Galois representation). The classification was fully known when p>2, and for connected p-divisible groups and finite flat group schemes for any p. (Both cases are due to Kisin.) So we focus on the case with p=2, and will explain the motivation and application of the classification, as well as the sketch of the proof (especially when p=2).
Independently, Eike Lau generalized display theory to arbitrary p-divisible groups (allowing p=2). Our approach differs from Lau's and we additionally recover the Tate module from the classification, while Lau's proved the classification over more general base without recovering Tate module from the classification.

### 2010N820ij 16:0017:00

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Matthias Strauch iIndiana Universityj
p-adic representations of division algebras: homotopy theory and the p-adic Langlands program
Tv
We will first outline a conjectural formalism of a p-adic Langlands correspondence (following work of Breuil and Breuil/Schneider). Then we will sketch constructions of representations of GL(2) and of quaternion division algebras D using rigid analytic moduli spaces (the so-called Drinfeld and Lubin-Tate towers). In the second part of the talk I will try to explain why homotopy theorists are interested in p-adic representations of D* (called Morava stabilizer groups in stable homotopy theory). We will finish by raising some questions about possible links between the two theories (mentioned in the title).

### 2010N79ij 16:3017:30

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Jae-Hyun Yang iInha Universityj
Derivatives of L-Functions
Tv
In this talk, I discuss derivatives of the Riemann zeta function, the Hasse-Weil L-function and some other important L-functions. I also review the Gross-Zagier formula due to B. Gross, D. Zagier and S. Zhang and the recent work of J. Bruinier and T. Yang about the relation between Faltings heights and derivatives of certain L-functions.

### 2010N618ij 15:3016:30, 16:4517:45

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Andreas Langer iUniversity of Exeterj
A de Rham-Witt complex for rigid cohomology
Tv
For a smooth scheme X over a perfect field of char p, we construct an overconvergent de Rham-Witt complex as a differential graded algebra over the ring of overconvergent Witt-vectors. The complex is suitable to compute the Monsky-Washnitzer cohomology if X is affine and the rigid cohomology if X is quasiprojective.
u
O} m i吔j
Cuspidal representations in the l-adic cohomology of the Rapoport-Zink space for GSp(4)
Tv
Rapoport-ZinkԂƂ́Ct\t pQ̏ʑ̃WCԂłCul̂̋ǏłƂ݂ȂƂłD̍uł́CGSp(4)ɑ΂Rapoport-Zink Ԃ l iRzW[ɊւčŋߍsCɓNjƂ̋ɂĕ񍐂D藝́CRapoport-ZinkiRapoport-Zink Ԃ̃Wbh͓I핢̎ˉenj i RpNg l iRzW[ƂēGSp4(Qp)̃X[Y\̕ɏ_\̂ i = 2,3,4 ̏ꍇɌƂ̂łDؖɂẮCuҎgɂēꂽאڗ֑̂̕ώ킪{IɗpD
Tvipj
Rapoport-Zink spaces are certain moduli spaces of quasi-isogenies of p-divisible groups with additional structures and can be regarded as local analogues of Shimura varieties. In this talk, I will report on my recent work with Tetsushi Ito on the l-adic cohomology of the Rapoport-Zink space for GSp(4). We prove that the smooth representation of GSp4(Qp) obtained as the i-th compactly supported l-adic cohomology of the Rapoport-Zink tower (a system of rigid analytic covering of the Rapoport-Zink spaces) has no quasi-cuspidal subquotient unless i = 2,3,4. In the course of the proof, the variants of formal nearby cycle introduced by myself play essential roles.

### 2010N514ij 16:0017:00

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V [ id@wj
W[Ȑ X_0ˆ+(N) 2̒l_ɂ
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W[ȐX_0(N)Atkin-Lehner involution w_Nɂ鏤X_0ˆ+(N)ƂB Nɑ΂āẢX_0ˆ+(N)2̒l_̓JXvCM_݂̂ł邱ƂB

### 2010N416ij 15:3017:00

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ؑ r iLwwȁj
Aˆ1zgs[@ƂĂMotivic Chow Series̗L
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َˉe㐔l̂Chow Motiveɑ΂ču҂́uL\zvoAȌΏۂƂĂB ̗\z΁AMotivic Zeta SeriesL֐ƂȂ邱Ƃ]AႦΗL̏ł͂Weil\z̐ƌȂƂłB Motivic Zeta Series ͌̑㐔l̂̑Ώ̐ςChow Motivešaƍl邱ƂłB
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### 2010N219ij 15:3016:30C16:4517:45

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Chieh-Yu Chang iNCTS and National Central Univ.j
Algebraic independence of the special values of Drinfeld modular forms at CM points
Tv
Let A be a polynomial ring in one variable over a finite field and let k be its fraction field. Let f be a Drinfeld modular form of nonzero weight for a congruence subgroup of GL(2,A) so that the coefficients of the expansion of f at infinity are algebraic over k. We consider n CM points on the Drinfeld upper half plane for which the corresponding CM fields are pairwise distinct. If f is non-vanishing at these n CM points, then we prove that the values of f at these CM points are algebraically independent over k.
u
V rY iL嗝j
Quasi-weak equivalences in complicial exact categories (joint work with Satoshi Mochizuki)
Tv
Ŝ̌̕ɋ[^ (quasi-isomorphism) ƂTÔƓlɁA 㓯ltSiႵ́A Waldhausen jɑ΂Ă̂̌̕Ɂu[㓯lvȂ㓯l𓱓. ̋[㓯ltɂ邱ƂŐVȓiOpj\ł. ʂɊŜ̌̕Ƌ[^͎㓯ltSƌȂ̂, ꂩXɓd̂̌ɋ[[^AOd̂̌ɋ[ˆ3^A[Iɒ邱ƂoA t铱Ƃďuv𓾂. pƂĊSɑ΂镉̑㐔I K Q̍ Grothendieck QŋLqł邱ƁA ܂ K Q邽߂̕Kv\͂荂ŕ\邱ƂЉ.
Tvipj
As quasi-isomorphisms in the category of chain complexes, I introduce the notion of "quasi-weak equivalences" associated with weak equivalences in an exact category (or some kind of biWaldhausen categories). The derived category of an exact category with weak equivalences is obtained by formally inverting such quasi-weak equivalences in the category of chain complexes. As applications, we obtain a delooping the K-theory for exact categories and a condition on the negative K-groups to be trivial.

### 2009N1218ij 15:3016:30

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Hoon Hong iNorth Carolina State Universityj
Connectivity in Semialgebraic Sets
Tv
A semialgebraic set is a subset of real space defined by polynomial equations and inequalities. A semialgebraic set is a union of finitely many maximally connected components. In this talk, we consider the problem of deciding whether two given points in a semialgebraic set are connected, that is, whether the two points lie in a same connected component. In particular, we consider the semialgebraic set defined by f not equal 0 where f is a given bivariate polynomial. The motivation comes from the observation that many important/non-trivial problems in science and engineering can be often reduced to that of connectivity. Due to it importance, there has been intense research effort on the problem. We will describe a method based on gradient fields and provide a sketch of the proof of correctness based Morse complex. The method seems to be more efficient than the previous methods in practice.

### 2009N124ij 16:3017:30

[NVbvuIndustrious Number TheoryvƂ̍łD ƎԂႢ܂̂łӂD

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u ~ i吔j
On logarithmic extension of overconvergent isocrystals
Tv
We give a certain condition for an overconvergent isocrystal on a smooth variety over a field of characteristic p>0 to extend logarithmically to its smooth compactification whose complement is a simple normal crossing divisor. If time permits, we also give a ecut-by-curves criterionf for this condition.

### 2009N116ij 15:4516:45C17:0018:00

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c i吔j
ی^ Euler n L ֐̐ϕ
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ی^ Euler nƂ́AAf[QpxNgԂ̗̌łēKȊ֌Ŵ݂̂ƂłB ̍uł́Aی^ Euler nƁAɊ֌W L ֐̐ϕɂĂb܂B uɂb錋ʂ̑͋ߓq(IPMU) Ƃ̋ɂ蓾ꂽ̂łB
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ms i吔j
Ȑ̂overconvergent isocrystal̘Aڐɂ
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̍uł͋ȐFrobenius\Ƃ͌Ȃoverconvergent isocrystal̘Aڐ̌ʂЉƎv. Frobenius\ꍇBerthelot̗\zʂ̈ꕔƂȂĂ邪, Berthelot̗\zFrobenius\ȂꍇɂĂ̎^Ȃ. Frobenius\ȂꍇBerthelot\z͂ǂ̂悤ȌɂȂׂl@̌ʂɂĘbƎvB

### 2009N112ij 15:3017:00

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RIq isww@wȁj
Local B-model and Mixed Hodge Structure
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Local mirror symmetry is a variant of mirror symmetry derived from mirror symmetry of toric Calabi--Yau hypersurfaces. Its statement is as follows. Take a 2-dimensional reflexive polyhedron (e.g the convex hull of (1,0),(0,1),(-1,-1) ). On one side, one can associate to this a toric surface whose fan is generated by integral points of the polyhedron (e.g. P^2), and its local Gromov--Witten invariants (local A-model). On other side , one can associate an affine hypersurface C in 2- dimensional algebraic torus T^2 whose defining equation is the sum of Laurent monomials corresponding to integral points of the given polyhedron, and the relative cohomology group H^2(T^2, C) (local B-model). The both of them are closely related to@a system of differential equations associated to the polyhedron@called the A-hypergeometric system due to Gel'fand, Kapranov, Zelevinsky. As to the local B-model, the (V)MHS of H^2(T^2,C) has been studied by Batyrev and Stienstra. In the joint work with Satoshi Minabe (arXiv:0907.4108), we defined, using their results, an analogue of the Yukawa coupling whose direct definition was not known so far. In this talk, I explain these mixed Hodge theoretic aspects of the local B-model.

### 2009N1023ij 15:4516:45C17:0018:00

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Zariski density of two dimensional cristalline representations
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On the stable reduction of X_0(p^4)
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Recently Coleman-McMurdy found the stable reduction of X_0(p^3) based on rigid geometry and using Gross-Hopkins theory to analyze the supersingular locus. Furthermore, McMurdy conjecture on the stable reduction of X_0(p^4). We found an explicit computation of "new components" found by Coleman-McMurdy in the stable reduction of X_0(p^3) without using Gross-Hopkins theory. We found new components appearing in the stable reduction in X_0(p^4) which does not appear in the conjecture of McMurdy. We will talk on these topics.

### 2009N1021ij 11:0012:00

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Michel Waldschmidt ip 6 wj
On the Markoff equation x^2+y^2+z^2=3xyz
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It is easy to check that the equation x^2+y^2+z^2=3xyz, where the three unknowns x,y,z are positive integers, has infinitely many solutions. There is a simple algorithm which produces all of them. However,this does not answer to all questions on this equation: in particular Frobenius asked whether it is true that for each integer z>0, there is at most one pair (x,y) such that x<y<z and (x,y,z) is a solution. This question is an active research topic nowadays. Markoff's equation occurred initially in the study of minima of quadratic forms at the end of the XIX-th century and the beginning of the XX-th century. It was investigated by many a mathematician, including Lagrange, Hermite,Korkine, Zolotarev, Markoff, Frobenius, Hurwitz, Cassels. The solutions are related with the Lagrange-Markoff spectrum, which consists of those quadratic numbers which are badly approximable by rational numbers. It occurs also in other parts of mathematics, in particular free groups, Fuchsian groups and hyperbolic Riemann surfaces (Ford, Lehner, Cohn, Rankin, Conway, Coxeter, Hirzebruch and Zagier...). We discuss some aspects of this topic without trying to cover all of them.
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