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Seminar information archive
Seminar information archive ～06/10｜Today's seminar 06/11 | Future seminars 06/12～
2025/06/10
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Nobuyuki Oshima (Faculty of Engineering, Hokkaido University)
Immersed-boundary Navier-Stokes equation and its application to image data (Japanese)
Nobuyuki Oshima (Faculty of Engineering, Hokkaido University)
Immersed-boundary Navier-Stokes equation and its application to image data (Japanese)
Tuesday Seminar on Topology
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Takayuki Morifuji (Keio University)
Bell polynomials and hyperbolic volume of knots (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Takayuki Morifuji (Keio University)
Bell polynomials and hyperbolic volume of knots (JAPANESE)
[ Abstract ]
In this talk, we introduce two volume formulas for hyperbolic knot complements using Bell polynomials. The first applies to hyperbolic fibered knots and expresses the volume of the complement in terms of the trace of the monodromy matrix. The second provides a formula for the volume of general hyperbolic knot complements based on a weighted adjacency matrix. This talk is based on joint work with Hiroshi Goda.
[ Reference URL ]In this talk, we introduce two volume formulas for hyperbolic knot complements using Bell polynomials. The first applies to hyperbolic fibered knots and expresses the volume of the complement in terms of the trace of the monodromy matrix. The second provides a formula for the volume of general hyperbolic knot complements based on a weighted adjacency matrix. This talk is based on joint work with Hiroshi Goda.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie Groups and Representation Theory
15:30-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Joint with FJ-LMI Seminar.
Paolo Ciatti (University of Padua)
Spectral estimates on the Heisenberg group (English)
Joint with FJ-LMI Seminar.
Paolo Ciatti (University of Padua)
Spectral estimates on the Heisenberg group (English)
[ Abstract ]
In this talk we will discuss some estimates concerning the spectral projections of the sub-Laplacian on the Heisenberg group. We will also consider some open problems and formulate a conjecture, providing some motivation for it.
In this talk we will discuss some estimates concerning the spectral projections of the sub-Laplacian on the Heisenberg group. We will also consider some open problems and formulate a conjecture, providing some motivation for it.
Algebraic Geometry Seminar
14:00-15:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Meng Chen (Fudan University)
Some new methods in estimating the lower bound of the canonical volume of 3-folds of general type
Meng Chen (Fudan University)
Some new methods in estimating the lower bound of the canonical volume of 3-folds of general type
[ Abstract ]
We introduce some new advance in estimating the lower bound of the canonical volume of 3-folds of general type with very small geometric genus. This topic covers a joint work with Jungkai A. Chen, Yong Hu and Chen Jiang.
We introduce some new advance in estimating the lower bound of the canonical volume of 3-folds of general type with very small geometric genus. This topic covers a joint work with Jungkai A. Chen, Yong Hu and Chen Jiang.
Algebraic Geometry Seminar
16:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Xun Yu (Tianjin University)
On the real forms of smooth complex projective varieties
Xun Yu (Tianjin University)
On the real forms of smooth complex projective varieties
[ Abstract ]
The real form problem asks how many different ways one can describe a given complex variety by polynomial equations with real coefficients, up to isomorphisms over the real number field. In this talk, I will discuss some recent results about real forms of smooth complex projective varieties. This talk is based on my joint works with T.-C. Dinh, C. Gachet, G. van der Geer, H.-Y. Lin, K. Oguiso, and L. Wang.
The real form problem asks how many different ways one can describe a given complex variety by polynomial equations with real coefficients, up to isomorphisms over the real number field. In this talk, I will discuss some recent results about real forms of smooth complex projective varieties. This talk is based on my joint works with T.-C. Dinh, C. Gachet, G. van der Geer, H.-Y. Lin, K. Oguiso, and L. Wang.
Tokyo-Nagoya Algebra Seminar
15:30-17:00 Online
Mohamad Haerizadeh (Univeristy of Tehran)
Generic decompositions of g-vectors (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Mohamad Haerizadeh (Univeristy of Tehran)
Generic decompositions of g-vectors (English)
[ Abstract ]
In this talk, we discuss the role of g-vectors in the representation theory of algebras. Specifically, we describe how generic decompositions of g-vectors yield decompositions of generically τ-reduced components of representation varieties and vice versa. This connection allows us to provide a partial answer to the Cerulli-Labardini-Schröer conjecture concerning the number of direct summands of generically τ-reduced components of representation varieties.
Furthermore, we examine the cones of g-vectors, demonstrating that they are both rational and simplicial. We establish that g-vectors satisfy the ray condition if they are sufficiently far from the origin. These results enable us to generalize several results by Asai and Iyama concerning TF-equivalence classes of g-vectors. Therefore, our consequences can be utilized to study the wall and chamber structures of finite-dimensional algebras. This is joint work with Siamak Yassemi.
Zoom ID 844 4810 7612 Password 275169
[ Reference URL ]In this talk, we discuss the role of g-vectors in the representation theory of algebras. Specifically, we describe how generic decompositions of g-vectors yield decompositions of generically τ-reduced components of representation varieties and vice versa. This connection allows us to provide a partial answer to the Cerulli-Labardini-Schröer conjecture concerning the number of direct summands of generically τ-reduced components of representation varieties.
Furthermore, we examine the cones of g-vectors, demonstrating that they are both rational and simplicial. We establish that g-vectors satisfy the ray condition if they are sufficiently far from the origin. These results enable us to generalize several results by Asai and Iyama concerning TF-equivalence classes of g-vectors. Therefore, our consequences can be utilized to study the wall and chamber structures of finite-dimensional algebras. This is joint work with Siamak Yassemi.
Zoom ID 844 4810 7612 Password 275169
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025/06/09
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Nobuhiro Honda (Institute of Science Tokyo)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Nobuhiro Honda (Institute of Science Tokyo)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Tokyo Probability Seminar
17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)
The lecture is starting late. No Tea Time today.
Kenkichi Tsunoda (Kyushu University)
粒子系に対する静的な揺らぎ
The lecture is starting late. No Tea Time today.
Kenkichi Tsunoda (Kyushu University)
粒子系に対する静的な揺らぎ
[ Abstract ]
非平衡定常状態は数理物理の問題として様々な文脈の中で研究されている。非平衡定常状態とはカレントは0でないが時間に対して不変な状態であり、相互作用粒子系においては系の定常測度として定義される。非平衡定常状態の解析で難しい問題点として、その明示的な具体形が知られていないことや定常測度が粒子系に対して可逆でないことなどがあげられる。そのため非平衡定常状態の解析は容易ではないが、一般的な手法として対応するdynamicsに対する解析を用いる方法がある。本講演では粒子数密度に対する揺らぎの問題について焦点を当て、境界で流入・流出のある排他過程やGlauber+Kawasaki過程に対してその手法を解説する。
非平衡定常状態は数理物理の問題として様々な文脈の中で研究されている。非平衡定常状態とはカレントは0でないが時間に対して不変な状態であり、相互作用粒子系においては系の定常測度として定義される。非平衡定常状態の解析で難しい問題点として、その明示的な具体形が知られていないことや定常測度が粒子系に対して可逆でないことなどがあげられる。そのため非平衡定常状態の解析は容易ではないが、一般的な手法として対応するdynamicsに対する解析を用いる方法がある。本講演では粒子数密度に対する揺らぎの問題について焦点を当て、境界で流入・流出のある排他過程やGlauber+Kawasaki過程に対してその手法を解説する。
2025/06/06
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Tomoki Yoshida (Waseda University)
Bridgeland Stability of Sheaves on del Pezzo Surface of Picard Rank Three
Tomoki Yoshida (Waseda University)
Bridgeland Stability of Sheaves on del Pezzo Surface of Picard Rank Three
[ Abstract ]
Bridgeland stability is a notion of stability for objects in a triangulated category, particularly in the bounded derived category of coherent sheaves. Unlike classical sheaf stability, it is often unclear whether fundamental sheaves, such as line bundles, are (semi)stable with respect to a given Bridgeland stability condition. In this talk, we focus on the del Pezzo surface of Picard rank three and study the Bridgeland stability of its line bundles and certain torsion sheaves. More precisely, we first determine the maximal destabilizing objects for line bundles and then outline our proof strategy in the torsion case.
This talk is based on arXiv:2502.18894, which is joint work with Yuki Mizuno.
Bridgeland stability is a notion of stability for objects in a triangulated category, particularly in the bounded derived category of coherent sheaves. Unlike classical sheaf stability, it is often unclear whether fundamental sheaves, such as line bundles, are (semi)stable with respect to a given Bridgeland stability condition. In this talk, we focus on the del Pezzo surface of Picard rank three and study the Bridgeland stability of its line bundles and certain torsion sheaves. More precisely, we first determine the maximal destabilizing objects for line bundles and then outline our proof strategy in the torsion case.
This talk is based on arXiv:2502.18894, which is joint work with Yuki Mizuno.
2025/06/05
Geometric Analysis Seminar
14:00-16:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Chao Li (New York University) 14:00-15:00
On the topology of stable minimal hypersurfaces in a homeomorphic $S^4$ (英語)
Poincar\'e-Einstein manifolds: conformal structure meets metric geometry (英語)
Chao Li (New York University) 14:00-15:00
On the topology of stable minimal hypersurfaces in a homeomorphic $S^4$ (英語)
[ Abstract ]
Given an $n$-dimensional manifold (with $n$ at least $4$), it is generally impossible to control the topology of a homologically minimizing hypersurface $M$. In this talk, we construct stable (or locally minimizing) hypersurfaces with optimal restrictions on its topology in a $4$-manifold $X$ with natural curvature conditions (e.g. positive scalar curvature), provided that $X$ admits certain embeddings into a homeomorphic $S^4$. As an application, we obtain black hole topology theorems in such $4$-dimensional asymptotically flat manifolds with nonnegative scalar curvature. This is based on joint work with Boyu Zhang.
Ruobing Zhang (University of Wisconsin–Madison) 15:30-16:30Given an $n$-dimensional manifold (with $n$ at least $4$), it is generally impossible to control the topology of a homologically minimizing hypersurface $M$. In this talk, we construct stable (or locally minimizing) hypersurfaces with optimal restrictions on its topology in a $4$-manifold $X$ with natural curvature conditions (e.g. positive scalar curvature), provided that $X$ admits certain embeddings into a homeomorphic $S^4$. As an application, we obtain black hole topology theorems in such $4$-dimensional asymptotically flat manifolds with nonnegative scalar curvature. This is based on joint work with Boyu Zhang.
Poincar\'e-Einstein manifolds: conformal structure meets metric geometry (英語)
[ Abstract ]
A Poincar\'e-Einstein manifold is a complete non-compact Einstein manifold with negative scalar curvature which can be conformally deformed to a compact manifold with boundary, called the conformal boundary or conformal infinity. Naturally, such a space is associated with a conformal structure on the conformal infinity. A fundamental theme in studying these geometric objects is to relate the Riemannian geometric data of the Einstein metric to the conformal geometric data at infinity which is also called the AdS/CFT correspondence in theoretical physics.
In this talk, we will explore some new techniques from the metric geometric point of view, by which one can establish some new rigidity, quantitative rigidity, and regularity results.
A Poincar\'e-Einstein manifold is a complete non-compact Einstein manifold with negative scalar curvature which can be conformally deformed to a compact manifold with boundary, called the conformal boundary or conformal infinity. Naturally, such a space is associated with a conformal structure on the conformal infinity. A fundamental theme in studying these geometric objects is to relate the Riemannian geometric data of the Einstein metric to the conformal geometric data at infinity which is also called the AdS/CFT correspondence in theoretical physics.
In this talk, we will explore some new techniques from the metric geometric point of view, by which one can establish some new rigidity, quantitative rigidity, and regularity results.
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Norihisa Ioku (Tohoku University)
Multiplicity of singular solutions for semilinear elliptic equations with superlinear source terms (Japanese)
Norihisa Ioku (Tohoku University)
Multiplicity of singular solutions for semilinear elliptic equations with superlinear source terms (Japanese)
[ Abstract ]
The structure of singular solutions to semilinear elliptic equations has been well understood in the case of power-type nonlinearities in three or higher dimensions. In this talk, we introduce a classification of general monotone increasing nonlinearities based on their growth rates, and then explain a method for constructing radially symmetric singular solutions according to this classification. In particular, we present recent results on the multiplicity of singular solutions in the sub-Sobolev critical regime. This talk is based on a joint work with Professor Yohei Fujishima (Shizuoka University).
The structure of singular solutions to semilinear elliptic equations has been well understood in the case of power-type nonlinearities in three or higher dimensions. In this talk, we introduce a classification of general monotone increasing nonlinearities based on their growth rates, and then explain a method for constructing radially symmetric singular solutions according to this classification. In particular, we present recent results on the multiplicity of singular solutions in the sub-Sobolev critical regime. This talk is based on a joint work with Professor Yohei Fujishima (Shizuoka University).
2025/06/03
Operator Algebra Seminars
16:45-18:15 Room #117 (Graduate School of Math. Sci. Bldg.)
Takehiko Mori (Chiba University)
Application of Operator Theory for the Collatz Conjecture
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Takehiko Mori (Chiba University)
Application of Operator Theory for the Collatz Conjecture
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Infinite Analysis Seminar Tokyo
15:00-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Veronica Fantini (Laboratoire Mathématique Orsay)
Modular resurgence (English)
https://sites.google.com/view/vfantini/home-page
Veronica Fantini (Laboratoire Mathématique Orsay)
Modular resurgence (English)
[ Abstract ]
Quantum modular forms were introduced by Zagier in 2010 to characterize the failure of modularity of certain q-series. Since then, different examples of quantum modular forms have also been studied in complex Chern-Simons theory and, more recently, in topological string theory on local Calabi-Yau 3folds. This talk aims to discuss the approach of resurgence to the study of a class of quantum modular forms. More precisely, I will present modular resurgence structures and illustrate their main properties. This is based on arXiv:2404.11550.
[ Reference URL ]Quantum modular forms were introduced by Zagier in 2010 to characterize the failure of modularity of certain q-series. Since then, different examples of quantum modular forms have also been studied in complex Chern-Simons theory and, more recently, in topological string theory on local Calabi-Yau 3folds. This talk aims to discuss the approach of resurgence to the study of a class of quantum modular forms. More precisely, I will present modular resurgence structures and illustrate their main properties. This is based on arXiv:2404.11550.
https://sites.google.com/view/vfantini/home-page
Tuesday Seminar on Topology
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Tatsuo Suwa (Hokkaido University)
Localized intersection product for maps and applications (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Tatsuo Suwa (Hokkaido University)
Localized intersection product for maps and applications (JAPANESE)
[ Abstract ]
We define localized intersection product in manifolds using combinatorial topology, which corresponds to the cup product in relative cohomology via the Alexander duality. It is extended to localized intersection product for maps. Combined with the relative Cech-de Rham cohomology, it is effectively used in the residue theory of vector bundles and coherent sheaves. As an application, we have the functoriality of Baum-Bott residues of singular holomorphic foliations under certain conditions, which yields answers to problems and conjectures posed by various authors concerning singular holomorphic foliations and complex Poisson structures. This includes a joint work with M. Correa.
References
[1] M. Correa and T. Suwa, On functoriality of Baum-Bott residues, arXiv:2501.15133.
[2] T. Suwa, Complex Analytic Geometry - From the Localization Viewpoint,
World Scientific, 2024.
[ Reference URL ]We define localized intersection product in manifolds using combinatorial topology, which corresponds to the cup product in relative cohomology via the Alexander duality. It is extended to localized intersection product for maps. Combined with the relative Cech-de Rham cohomology, it is effectively used in the residue theory of vector bundles and coherent sheaves. As an application, we have the functoriality of Baum-Bott residues of singular holomorphic foliations under certain conditions, which yields answers to problems and conjectures posed by various authors concerning singular holomorphic foliations and complex Poisson structures. This includes a joint work with M. Correa.
References
[1] M. Correa and T. Suwa, On functoriality of Baum-Bott residues, arXiv:2501.15133.
[2] T. Suwa, Complex Analytic Geometry - From the Localization Viewpoint,
World Scientific, 2024.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/06/02
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Wai-Kit Lam (National Taiwan University)
Disorder monomer-dimer model and maximum weight matching
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Wai-Kit Lam (National Taiwan University)
Disorder monomer-dimer model and maximum weight matching
[ Abstract ]
Given a finite graph, one puts i.i.d. weights on the edges and i.i.d. weights on the vertices. For a (partial) matching on this graph, define the weight of the matching by adding all the weights of the edges in the matching together with the weights of the unmatched vertices. One would like to understand how the maximum weight behaves as the size of the graph becomes large. The talk will be divided into two parts. In the first part, we consider the "positive temperature" case (a.k.a. the disorder monomer-dimer model). We show that the model exhibits correlation decay, and from this one can prove a Gaussian central limit theorem for the associated free energy. In the second part, we will focus on the "zero temperature" case, the maximum weight matching. We show that if the edge weights are exponentially distributed, and if the vertex weights are absent, then there is also correlation decay for a certain class of graphs. This correlation decay allows us to define the maximum weight matching on some infinite graphs and also prove limit theorems for the maximum weight matching. Joint work with Arnab Sen (Minnesota).
Given a finite graph, one puts i.i.d. weights on the edges and i.i.d. weights on the vertices. For a (partial) matching on this graph, define the weight of the matching by adding all the weights of the edges in the matching together with the weights of the unmatched vertices. One would like to understand how the maximum weight behaves as the size of the graph becomes large. The talk will be divided into two parts. In the first part, we consider the "positive temperature" case (a.k.a. the disorder monomer-dimer model). We show that the model exhibits correlation decay, and from this one can prove a Gaussian central limit theorem for the associated free energy. In the second part, we will focus on the "zero temperature" case, the maximum weight matching. We show that if the edge weights are exponentially distributed, and if the vertex weights are absent, then there is also correlation decay for a certain class of graphs. This correlation decay allows us to define the maximum weight matching on some infinite graphs and also prove limit theorems for the maximum weight matching. Joint work with Arnab Sen (Minnesota).
2025/05/30
Colloquium
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
John A G Roberts (School of Mathematics and Statistics, UNSW Sydney / Graduate School of Mathematical Sciences, The University of Tokyo)
Arithmetic and geometric aspects of the (symbolic) dynamics of piecewise-linear maps (English)
John A G Roberts (School of Mathematics and Statistics, UNSW Sydney / Graduate School of Mathematical Sciences, The University of Tokyo)
Arithmetic and geometric aspects of the (symbolic) dynamics of piecewise-linear maps (English)
[ Abstract ]
We study a family of planar area-preserving maps, described by different $SL(2,\mathbb{R})$ matrices on the right and left half-planes. Such maps, studied extensively by Lagarias and Rains in 2005, can support periodic and quasiperiodic dynamics with a foliation of the plane by invariant curves. The parameter space is two dimensional (the parameters being the traces of the two matrices) and the set of parameters for which an initial condition on the half-plane boundary returns to it are algebraic “critical” curves, described by the symbolic dynamics of the itinerary between the boundaries. An important component of the planar dynamics is the rotational dynamics it induces on the unit circle. The study of the arithmetic, algebraic, and geometric aspects of the planar and circle (symbolic) dynamics has connections to various parts of number theory and geometry, which I will mention. These include: Farey sequences; continued fraction expansions and continuant polynomials; the character variety of group representations in $SL(2, \mathbb{C})$ and $PSL(2, \mathbb{C})$; and the group of polynomial diffeomorphisms of $\mathbb{C}^3$ preserving the Fricke-Vogt invariant $x^2 + y^2 + z^2 - xyz$.
This is joint work with Asaki Saito (Hakodate) and Franco Vivaldi (London).
We study a family of planar area-preserving maps, described by different $SL(2,\mathbb{R})$ matrices on the right and left half-planes. Such maps, studied extensively by Lagarias and Rains in 2005, can support periodic and quasiperiodic dynamics with a foliation of the plane by invariant curves. The parameter space is two dimensional (the parameters being the traces of the two matrices) and the set of parameters for which an initial condition on the half-plane boundary returns to it are algebraic “critical” curves, described by the symbolic dynamics of the itinerary between the boundaries. An important component of the planar dynamics is the rotational dynamics it induces on the unit circle. The study of the arithmetic, algebraic, and geometric aspects of the planar and circle (symbolic) dynamics has connections to various parts of number theory and geometry, which I will mention. These include: Farey sequences; continued fraction expansions and continuant polynomials; the character variety of group representations in $SL(2, \mathbb{C})$ and $PSL(2, \mathbb{C})$; and the group of polynomial diffeomorphisms of $\mathbb{C}^3$ preserving the Fricke-Vogt invariant $x^2 + y^2 + z^2 - xyz$.
This is joint work with Asaki Saito (Hakodate) and Franco Vivaldi (London).
2025/05/27
Tuesday Seminar of Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
TAIRA Koichi (Kyushu University)
Semiclassical behaviors of matrix-valued operators (Japanese)
TAIRA Koichi (Kyushu University)
Semiclassical behaviors of matrix-valued operators (Japanese)
2025/05/26
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shin-ichi Matsumura (Tohoku Univ.)
Fundamental groups of compact K\"ahler manifolds with semi-positive holomorphic sectional curvature (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Shin-ichi Matsumura (Tohoku Univ.)
Fundamental groups of compact K\"ahler manifolds with semi-positive holomorphic sectional curvature (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/05/23
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Takuya Miyamoto (University of Tokyo)
Pathology of formal locally-trivial
deformations in positive characteristic
Takuya Miyamoto (University of Tokyo)
Pathology of formal locally-trivial
deformations in positive characteristic
[ Abstract ]
An infinitesimal deformation of an algebraic variety X is called (formally) locally trivial if it is Zariski-locally isomorphic to the trivial deformation. The locally trivial deformation functor of X is the subfunctor of the usual deformation functor associated with X consisting of locally trivial deformations. In this talk, I will construct an explicit example that is an algebraic curve in positive characteristic whose locally trivial deformation functor does not satisfy Schlessinger’s first condition (H_1), in contrast to the complex/characteristic 0 case. In particular, this provides a negative answer to a question posed by H. Flenner and S. Kosarew. I will also mention recent progress on the structure of fibers of locally trivial deformation functors.
An infinitesimal deformation of an algebraic variety X is called (formally) locally trivial if it is Zariski-locally isomorphic to the trivial deformation. The locally trivial deformation functor of X is the subfunctor of the usual deformation functor associated with X consisting of locally trivial deformations. In this talk, I will construct an explicit example that is an algebraic curve in positive characteristic whose locally trivial deformation functor does not satisfy Schlessinger’s first condition (H_1), in contrast to the complex/characteristic 0 case. In particular, this provides a negative answer to a question posed by H. Flenner and S. Kosarew. I will also mention recent progress on the structure of fibers of locally trivial deformation functors.
2025/05/21
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Toni Annala (University of Chicago)
A¹-Colocalization and Logarithmic Cohomology Theories
https://tannala.com/
Toni Annala (University of Chicago)
A¹-Colocalization and Logarithmic Cohomology Theories
[ Abstract ]
In recent joint work with Hoyois and Iwasa, we discovered that non-A¹-invariant motivic homotopy theory offers a new lens for understanding logarithmic cohomology theories. Central to this perspective is A¹-colocalization, which produces a cohomology theory whose value on a smooth scheme U agrees with the "logarithmic cohomology" of a good compactification (X,D). In many examples, including de Rham and crystalline cohomology, the quotation marks can be dropped, as A¹-colocalization recovers the classical logarithmic cohomology groups. I will explain this connection and, time permitting, sketch a proof of the duality theorem underlying this phenomenon, which states that smooth projective schemes have a dualizable motive.
[ Reference URL ]In recent joint work with Hoyois and Iwasa, we discovered that non-A¹-invariant motivic homotopy theory offers a new lens for understanding logarithmic cohomology theories. Central to this perspective is A¹-colocalization, which produces a cohomology theory whose value on a smooth scheme U agrees with the "logarithmic cohomology" of a good compactification (X,D). In many examples, including de Rham and crystalline cohomology, the quotation marks can be dropped, as A¹-colocalization recovers the classical logarithmic cohomology groups. I will explain this connection and, time permitting, sketch a proof of the duality theorem underlying this phenomenon, which states that smooth projective schemes have a dualizable motive.
https://tannala.com/
2025/05/20
Operator Algebra Seminars
16:45-18:15 Room #117 (Graduate School of Math. Sci. Bldg.)
Futaba Sato (the University of Tokyo)
Heat semigroups on quantum automorphism groups of finite dimensional C$^*$-algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Futaba Sato (the University of Tokyo)
Heat semigroups on quantum automorphism groups of finite dimensional C$^*$-algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Lie Groups and Representation Theory
15:30-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Masatoshi KITAGAWA (Institute of Mathematics for Industry, Kyushu University)
On the restriction of good filtration in the branching problem of reductive Lie groups (Japanese)
Masatoshi KITAGAWA (Institute of Mathematics for Industry, Kyushu University)
On the restriction of good filtration in the branching problem of reductive Lie groups (Japanese)
[ Abstract ]
In arXiv:2405.10382, a Cartan subalgebra related to the branching problem of reductive Lie groups was defined. It is considered to control the size and shape of the continuous spectrum in irreducible decompositions, and is defined using the support of the action of the center of the universal enveloping algebra. Except in special cases, direct computations from the definition of this Cartan subalgebra are difficult.
In this talk, I will present results on restrictions of good filtrations and show a relation between the associated varieties of representations and the Cartan subalgebra.
I will also discuss applications to the necessary condition for discrete decomposability and related conjectures by T. Kobayashi.
In arXiv:2405.10382, a Cartan subalgebra related to the branching problem of reductive Lie groups was defined. It is considered to control the size and shape of the continuous spectrum in irreducible decompositions, and is defined using the support of the action of the center of the universal enveloping algebra. Except in special cases, direct computations from the definition of this Cartan subalgebra are difficult.
In this talk, I will present results on restrictions of good filtrations and show a relation between the associated varieties of representations and the Cartan subalgebra.
I will also discuss applications to the necessary condition for discrete decomposability and related conjectures by T. Kobayashi.
2025/05/19
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yu Yasufuku (Waseda Univ.)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yu Yasufuku (Waseda Univ.)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/05/16
Seminar on Probability and Statistics
13:30-14:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Maud Delattre (INRAE)
Efficient precondition stochastic gradient descent for estimation in latent variables models (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/yixIylc3S8uJqOQ_Vqm_3Q
Maud Delattre (INRAE)
Efficient precondition stochastic gradient descent for estimation in latent variables models (English)
[ Abstract ]
Latent variable models are powerful tools for modeling complex phenomena involving in particular partially observed data, unobserved variables or underlying complex unknown structures. Inference is often difficult due to the latent structure of the model. To deal with parameter estimation in the presence of latent variables, well-known efficient methods exist, such as gradient-based and EM-type algorithms, but with practical and theoretical limitations. In this work, we propose as an alternative for parameter estimation an efficient preconditioned stochastic gradient algorithm.
Our method includes a preconditioning step based on a positive definite Fisher information matrix estimate. We prove convergence results for the proposed algorithm under mild assumptions for very general latent variable models. We illustrate through relevant simulations the performance of the proposed methodology in a nonlinear mixed-effects model.
[ Reference URL ]Latent variable models are powerful tools for modeling complex phenomena involving in particular partially observed data, unobserved variables or underlying complex unknown structures. Inference is often difficult due to the latent structure of the model. To deal with parameter estimation in the presence of latent variables, well-known efficient methods exist, such as gradient-based and EM-type algorithms, but with practical and theoretical limitations. In this work, we propose as an alternative for parameter estimation an efficient preconditioned stochastic gradient algorithm.
Our method includes a preconditioning step based on a positive definite Fisher information matrix estimate. We prove convergence results for the proposed algorithm under mild assumptions for very general latent variable models. We illustrate through relevant simulations the performance of the proposed methodology in a nonlinear mixed-effects model.
https://u-tokyo-ac-jp.zoom.us/meeting/register/yixIylc3S8uJqOQ_Vqm_3Q
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Keita Goto (University of Tokyo)
Berkovich geometry and SYZ fibration
Keita Goto (University of Tokyo)
Berkovich geometry and SYZ fibration
[ Abstract ]
The SYZ fibration refers to a special Lagrangian torus fibration on a Calabi–Yau manifold and has been extensively studied in the context of mirror symmetry.
In particular, for a degenerating family of Calabi--Yau manifolds, a family of SYZ fibrations defined on each fiber, away from a subset of sufficiently small measure, plays a central role.
However, the existence of such fibrations remains an open problem, known as the metric SYZ conjecture.
To approach this problem, formal analytic techniques are particularly effective, and Berkovich geometry lies at their foundation.
In this talk, I will explain Yang Li’s "comparison property," a sufficient condition for the conjecture, and present some related results I have been involved in. Along the way, I will also introduce some foundational ideas in Berkovich geometry.
The SYZ fibration refers to a special Lagrangian torus fibration on a Calabi–Yau manifold and has been extensively studied in the context of mirror symmetry.
In particular, for a degenerating family of Calabi--Yau manifolds, a family of SYZ fibrations defined on each fiber, away from a subset of sufficiently small measure, plays a central role.
However, the existence of such fibrations remains an open problem, known as the metric SYZ conjecture.
To approach this problem, formal analytic techniques are particularly effective, and Berkovich geometry lies at their foundation.
In this talk, I will explain Yang Li’s "comparison property," a sufficient condition for the conjecture, and present some related results I have been involved in. Along the way, I will also introduce some foundational ideas in Berkovich geometry.
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