## 過去の記録

#### 博士論文発表会

17:15-18:30   数理科学研究科棟(駒場) 118号室

An algebraic approach to Duflo's polynomial conjecture in the nilpotent case
(冪零の場合のDufloの多項式予想に対する代数的アプローチ）
(JAPANESE)

#### 博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 122号室

Hénon type elliptic equations with critical Sobolev growth
(臨界Sobolev指数を持つHénon 型楕円型方程式）
(JAPANESE)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 122号室

Binding stability of molecules in density-matrix-functional theories
(密度行列汎関数理論における分子の安定性)
(JAPANESE)

#### 博士論文発表会

15:45-17:00   数理科学研究科棟(駒場) 122号室

Long-range scattering problem and continuum limit of discrete Schrödinger operators
(離散シュレディンガー作用素の長距離散乱問題と連続極限)
(JAPANESE)

#### 博士論文発表会

17:15-18:30   数理科学研究科棟(駒場) 122号室

Localization in direction of Schrödinger operators with homogeneous potentials of order zero．
(0次斉次なポテンシャルを持つシュレディンガー作用素の方向局所化について)
(JAPANESE)

#### 博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 126号室

Constructions of various solutions for parabolic equations in mathematical biology and phase-field models
(数理生物学とフェイズフィールドモデルにおける放物型方程式に対する様々な解の構成）
(JAPANESE)

#### 博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 126号室

Spreading speeds and asymptotic profiles of solutions of the farmer and hunter-gatherer models
(農耕民族と狩猟採集民族モデルの解の広がり速度と漸近的形状)
(ENGLISH)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 126号室

A combinatorial study on K-theoretic k-Schur functions and stable Grothendieck polynomials
( K-理論的k-シューア関数と安定グロタンディーク多項式に関する組合せ論的研究)
(JAPANESE)

#### 博士論文発表会

15:45-17:00   数理科学研究科棟(駒場) 126号室

Equivariant Iwasawa theory for elliptic curves
(楕円曲線の同変岩澤理論）
(JAPANESE)

#### 博士論文発表会

17:15-18:30   数理科学研究科棟(駒場) 126号室

Some arithmetic properties of geodesic cycles on locally symmetric spaces
(局所対称空間上の測地的サイクルの数論的性質についての研究）
(JAPANESE)

### 2019年01月30日(水)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 126号室

2次元共形場理論を用いたトポロジカル相のモデルの構成 (Japanese)

### 2019年01月29日(火)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室

Logarithmic good reduction and the index (TBA)
[ 講演概要 ]
A proper smooth variety over a complete discrete valuation field is said to have (log) good reduction if it admits a proper (log) smooth model over the valuation ring (the log structure is given by the closed fiber). Monodromy criteria for good reduction and log good reduction have been studied. We study the log case by additional other conditions on geometric invariants such as the index of the variety (the minimal positive degree of a 0-cycle). In particular, we obtain a criterion for log good reduction of curves of genus one.

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Salvatore Stuvard 氏 (The University of Texas at Austin)
The regularity of area minimizing currents modulo $p$ (English)
[ 講演概要 ]
The theory of integer rectifiable currents was introduced by Federer and Fleming in the early 1960s in order to provide a class of generalized surfaces where the classical Plateau problem could be solved by direct methods. Since then, a number of alternative spaces of surfaces have been developed in geometric measure theory, as required for theory and applications. In particular, Fleming introduced currents modulo $2$ to treat non-orientable surfaces, and currents modulo $p$ (where $p \geq 2$ is an integer) to study more general surfaces occurring as soap films.
It is easy to see that, in general, area minimizing currents modulo $p$ need not be smooth surfaces. In this talk, I will sketch the proof of the following result, which achieves the best possible estimate for the Hausdorff dimension of the singular set of an area minimizing current modulo $p$ in the most general hypotheses, thus answering a question of White from the 1980s: if $T$ is an area minimizing current modulo $p$ of dimension $m$ in $R^{m+n}$, then $T$ is smooth at all its interior points, except those belonging to a singular set of Hausdorff dimension at most $m-1$.

### 2019年01月28日(月)

#### 東京確率論セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室

ランダム行列に関する普遍的な点過程間の遷移関係とその力学版 (JAPANESE)
[ 講演概要 ]
ランダム行列に関する無限粒子系の点過程として、Bessel点過程、サイン点過程、Airy点過程がよく知られている。これらは最初、Gaussianランダム行列モデルの固有値のスケーリング極限として得られたが、その後様々なモデルのスケーリング極限としても得られるという普遍性が明らかになった。この意味で、上記3つの点過程はランダム行列に関する典型的なモデルといえる。さらに、この3つは互いにスケーリング極限で結びついており、Bessel点過程を親玉とした遷移関係が存在することが知られている。今回の講演では、この点過程間の遷移関係が、点過程に自然に付随する確率力学にも遺伝することを導き、確率力学のレベルにおいてもBessel干渉型確率微分方程式を親玉とする遷移関係があることを紹介する。また時間が許す限り証明についても述べたい。

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Minimizing CM degree and slope stability of projective varieties (JAPANESE)
[ 講演概要 ]
Chow-Mumford (CM) line bundle is considered to play an important role in moduli problem for K-stable Fano varieties. In this talk, we consider a minimization problem of the degree of the CM line bundle among all possible fillings of a polarized family over a punctured curve. We show that such minimization implies the slope semistability of the fiber if the central fiber is smooth.

### 2019年01月22日(火)

#### 解析学火曜セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室

Construction of solutions to Schrodinger equations with sub-quadratic potential via wave packet transform (Japanese)
[ 講演概要 ]
In this talk, we consider linear Schrodinger equations with sub-quadratic potentials, which can be transformed by the wave packet transform with time dependent wave packet to a PDE of first order with inhomogeneous terms including unknown function and second derivatives of the potential. If the second derivatives of the potentials are bounded, the homogenous term of the first oder equation gives a construction of solutions to Schrodinger equations with sub-quadratic potentials by the similar way as in D. Fujiwara's work for Feynman path integral. We will show numerical computations by using our construction, if we have enough time.

### 2019年01月21日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
Nicholas James McCleerey 氏 (Northwestern University)
POLAR TRANSFORM AND LOCAL POSITIVITY FOR CURVES (ENGLISH)
[ 講演概要 ]
Using the duality of positive cones, we show that applying the polar transform from convexanalysis to local positivity invariants for divisors gives interesting and new local positivity invariantsfor curves. These new invariants have nice properties similar to those for divisors. In particular, thisenables us to give a characterization of the divisorial components of the non-K¨ahler locus of a big class. This is joint worth with Jian Xiao.

### 2019年01月16日(水)

#### 代数学コロキウム

18:00-19:00   数理科学研究科棟(駒場) 056号室
Lei Fu 氏 (Yau Mathematical Sciences Center, Tsinghua University)
[ 講演概要 ]
Using Dwork's trace formula, we express the exponential sum associated to a Laurent polynomial as the trace of a chain map on a twisted de Rham complex for the torus over the p-adic field. Treating the coefficients of the polynomial as parameters, we obtain the p-adic Gelfand-Kapranov-Zelevinsky (GKZ) system, which is a complex of D^\dagger-modules with Frobenius structure.

（本講演は「東京北京パリ数論幾何セミナー」として，インターネットによる東大数理，Morningside Center of Mathematics と IHES の双方向同時中継で行います．今回は北京からの中継です．）

### 2019年01月15日(火)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00

Generalized Dehn twists on surfaces and homology cylinders (JAPANESE)
[ 講演概要 ]
This is a joint work with Gwénaël Massuyeau (University of Burgundy). Lickorish's trick describes Dehn twists along simple closed curves on an oriented surface in terms of surgery of 3-manifolds. We discuss one possible generalization of this description to the situation where the curve under consideration may have self-intersections. Our result generalizes previously known computations related to the Johnson homomorphisms for the mapping class groups and for homology cylinders. In particular, we obtain an alternative and direct proof of the surjectivity of the Johnson homomorphisms for homology cylinders, which was proved by Garoufalidis-Levine and Habegger.

### 2019年01月09日(水)

#### 代数学コロキウム

17:00-18:00   数理科学研究科棟(駒場) 056号室
Laurent Berger 氏 (ENS de Lyon)
Formal groups and p-adic dynamical systems (ENGLISH)
[ 講演概要 ]
A formal group gives rise to a p-adic dynamical system. I will discuss some results about formal groups that can be proved using this point of view. I will also discuss the theory of p-adic dynamical systems and some open questions.

### 2019年01月08日(火)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
Marek Kaluba 氏 (Adam Mickiewicz Univeristy)
On property (T) for $\mathrm{Aut}(F_n)$ and $\mathrm{SL}_n(\mathbb{Z})$ (ENGLISH)
[ 講演概要 ]
We prove that $\mathrm{Aut}(F_n)$ has Kazhdan's property (T) for every $n \ge 6$. Together with a previous result of Kaluba, Nowak, and Ozawa, this gives the same statement for $n \ge 5$. We also provide explicit lower bounds for the Kazhdan constants of $\mathrm{SAut}(F_n)$ (with $n \ge 6$) and of $\mathrm{SL}_n(\mathbb{Z})$ (with $n \ge 3$) with respect to natural generating sets. In the latter case, these bounds improve upon previously known lower bounds whenever $n >6$.

### 2018年12月25日(火)

#### 解析学火曜セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室

Modified scattering for nonlinear dispersive equations with critical non-polynomial nonlinearities (Japanese)
[ 講演概要 ]
In this talk, I will introduce resent progress on modified scattering for Schrodinger equation and Klein-Gordon equation with a non-polynomial nonlinearity. We use Fourier series expansion technique to find the resonant part of the nonlinearity which produces phase correction factor.

#### 東京無限可積分系セミナー

16:00-17:00   数理科学研究科棟(駒場) 002号室

Q-operators for generalised eight vertex models associated
to the higher spin representations of the Sklyanin algebra. (ENGLISH)
[ 講演概要 ]
The Q-operator was first introduced by Baxter in 1972 as a
tool to solve the eight vertex model and recently attracts
attention from the representation theoretical viewpoint. In
this talk, we show that Baxter's apparently quite ad hoc and
technical construction can be generalised to the model
associated to the higher spin representations of the
Sklyanin algebra. If everybody in the audience understands Japanese, the talk
will be in Japanese.

### 2018年12月21日(金)

#### 代数幾何学セミナー

10:30-11:30   数理科学研究科棟(駒場) 123号室
Mattias Jonsson 氏 (Michigan)
Degenerations of p-adic volume forms (English)
[ 講演概要 ]
Let X be an n-dimensional smooth projective variety over a non-Archimedean local field K. Also fix a regular n-form on X. This data induces a positive measure on the space of K'-rational points for any finite extension K' of K. We describe the asymptotics, as K' runs through towers of finite extensions of K, in terms of Berkovich analytic geometry. This is joint work with Johannes Nicaise.

### 2018年12月20日(木)

#### トポロジー火曜セミナー

13:00-14:30   数理科学研究科棟(駒場) 056号室

Anderson Vera 氏 (Université de Strasbourg)
Johnson-type homomorphisms and the LMO functor (ENGLISH)
[ 講演概要 ]
One of the main objects associated to a surface S is the mapping class group MCG(S). This group plays an important role in the study of 3-manifolds. Reciprocally, the topological invariants of 3-manifolds can be used to obtain interesting representations of MCG(S).

One possible approach to the study of MCG(S) is to consider its action on the fundamental group P of the surface or on some subgroups of P. This way, we can obtain some kind of filtrations of MCG(S) and homomorphisms, called Johnson type homomorphisms, which take values in certain spaces of diagrams. These spaces of diagrams are quotients of the target space of the LMO functor. Hence it is natural to ask what is the relation between the Johnson type homomorphisms and the LMO functor. The answer is well known in the case of the Torelli group and the usual Johnson homomorphisms. In this talk we consider two other different filtrations of MCG(S) introduced by Levine and Habiro-Massuyeau. We show that the respective Johnson homomorphisms can also be deduced from the LMO functor.