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Seminar information archive
Seminar information archive ～04/19｜Today's seminar 04/20 | Future seminars 04/21～
Information Mathematics Seminar
16:50-18:20 Room #123 (Graduate School of Math. Sci. Bldg.)
Yasuhiko Ikematsu (Kyushu Univ.)
Recent progress in multivariate public key cryptography (Japanese)
Yasuhiko Ikematsu (Kyushu Univ.)
Recent progress in multivariate public key cryptography (Japanese)
[ Abstract ]
In this talk, I explain recent progress in multivariate public key cryptography (MPKC), mainly UOV and Rainbow signature schemes.
In this talk, I explain recent progress in multivariate public key cryptography (MPKC), mainly UOV and Rainbow signature schemes.
2022/11/16
Number Theory Seminar
17:00-18:00 Hybrid
Zijian Yao (University of Chicago)
The eigencurve over the boundary of the weight space (English)
Zijian Yao (University of Chicago)
The eigencurve over the boundary of the weight space (English)
[ Abstract ]
The eigencurve is a geometric object that p-adically interpolates eigenforms of finite slope. The global geometry of the eigencurve is somewhat mysterious, except that over the boundary, it is predicted to behave rather nicely (by the so-called Halo conjecture). This conjecture has been studied by Liu--Wan--Xiao for definite quaternion algebras. In this talk, we will report on some work in progress on this conjecture in the case of GL2. If time permits, we will discuss some generalizations towards groups beyond GL2. This is partially joint with H. Diao.
The eigencurve is a geometric object that p-adically interpolates eigenforms of finite slope. The global geometry of the eigencurve is somewhat mysterious, except that over the boundary, it is predicted to behave rather nicely (by the so-called Halo conjecture). This conjecture has been studied by Liu--Wan--Xiao for definite quaternion algebras. In this talk, we will report on some work in progress on this conjecture in the case of GL2. If time permits, we will discuss some generalizations towards groups beyond GL2. This is partially joint with H. Diao.
2022/11/15
Operator Algebra Seminars
16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Michiya Mori (Univ. Tokyo)
Ring isomorphisms of locally measurable operator algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Michiya Mori (Univ. Tokyo)
Ring isomorphisms of locally measurable operator algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Arthur Soulié (IBS Center for Geometry and Physics, POSTECH)
Stable cohomology of mapping class groups with some particular twisted contravariant coefficients (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Arthur Soulié (IBS Center for Geometry and Physics, POSTECH)
Stable cohomology of mapping class groups with some particular twisted contravariant coefficients (ENGLISH)
[ Abstract ]
The twisted cohomology of mapping class groups of compact orientable surfaces (with one boundary) is very difficult to compute generally speaking. In this talk, I will describe the computation of the stable cohomology algebra of these mapping class groups with twisted coefficients given by the first homology of the unit tangent bundle of the surface. This type of computation is out of the scope of the traditional framework for homological stability. Indeed, these twisted coefficients define a contravariant functor over the classical category associated to mapping class groups to study homological stability, rather than a covariant one. I will also present the computation of the stable cohomology algebras with with twisted coefficients given by the exterior powers and tensor powers of the first homology of the unit tangent bundle of the surface. All this represents a joint work with Nariya Kawazumi.
[ Reference URL ]The twisted cohomology of mapping class groups of compact orientable surfaces (with one boundary) is very difficult to compute generally speaking. In this talk, I will describe the computation of the stable cohomology algebra of these mapping class groups with twisted coefficients given by the first homology of the unit tangent bundle of the surface. This type of computation is out of the scope of the traditional framework for homological stability. Indeed, these twisted coefficients define a contravariant functor over the classical category associated to mapping class groups to study homological stability, rather than a covariant one. I will also present the computation of the stable cohomology algebras with with twisted coefficients given by the exterior powers and tensor powers of the first homology of the unit tangent bundle of the surface. All this represents a joint work with Nariya Kawazumi.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Algebraic Geometry Seminar
10:30-12:00 Room #ハイブリッド開催/002 (Graduate School of Math. Sci. Bldg.)
Chi-Kang Chang (NTU/Tokyo)
Positivity of anticanonical divisors in algebraic fibre spaces (日本語)
Chi-Kang Chang (NTU/Tokyo)
Positivity of anticanonical divisors in algebraic fibre spaces (日本語)
[ Abstract ]
It is known that the positivity of the anti-canonical divisor is an important property that is closely related to the geometric structure of a variety. Given an algebraic fibre space f : X → Y between normal projective varieties with mild singularities, and let F be a general fibre of f. In this talk, we will introduce results relating the positivity of −KX and −KY under some conditions on the asymptotic base loci of −KX. In particular, we will obtain an inequality between the anti-canonical Iitaka dimensions κ(X, −KX) ≤ κ(F, −KF ) + κ(Y, −KY ) under the assumption that the stable base locus B(−KX) does not dominant over Y .
It is known that the positivity of the anti-canonical divisor is an important property that is closely related to the geometric structure of a variety. Given an algebraic fibre space f : X → Y between normal projective varieties with mild singularities, and let F be a general fibre of f. In this talk, we will introduce results relating the positivity of −KX and −KY under some conditions on the asymptotic base loci of −KX. In particular, we will obtain an inequality between the anti-canonical Iitaka dimensions κ(X, −KX) ≤ κ(F, −KF ) + κ(Y, −KY ) under the assumption that the stable base locus B(−KX) does not dominant over Y .
2022/11/14
Seminar on Geometric Complex Analysis
15:00-16:30 Online
Hideki Miyach (Kanazawa University)
The double holomorphic tangent space of the Teichmueller spaces (Japanese)
https://forms.gle/hYT2hVhDE3q1wDSh6
Hideki Miyach (Kanazawa University)
The double holomorphic tangent space of the Teichmueller spaces (Japanese)
[ Abstract ]
The double holomorphic tangent space of a complex manifold is the holomorphic tangent space of the holomorphic tangent bundle of the complex manifold. In this talk, we will give an intrinsic description of the double tangent spaces of the Teichmueller spaces of closed Riemann surfaces of genus at least 2.
[ Reference URL ]The double holomorphic tangent space of a complex manifold is the holomorphic tangent space of the holomorphic tangent bundle of the complex manifold. In this talk, we will give an intrinsic description of the double tangent spaces of the Teichmueller spaces of closed Riemann surfaces of genus at least 2.
https://forms.gle/hYT2hVhDE3q1wDSh6
2022/11/10
Lectures
11:00-12:30 Online
Seminars by Professor O. Emanouilov (Colorado State Univ.)
Professor O. Emanouilov (Colorado State Univ.)
Inverse problems for partial differential equations: past and future works (English)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/88649482949?pwd=Yk9sNzJDNmNmZlRDeXAvcFFtcUkzUT09
Seminars by Professor O. Emanouilov (Colorado State Univ.)
Professor O. Emanouilov (Colorado State Univ.)
Inverse problems for partial differential equations: past and future works (English)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/88649482949?pwd=Yk9sNzJDNmNmZlRDeXAvcFFtcUkzUT09
2022/11/08
Operator Algebra Seminars
16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Ryoya Arimoto (RIMS, Kyoto Univ.)
On the type of the von Neumann algebra of an open subgroup of the Neretin group
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Ryoya Arimoto (RIMS, Kyoto Univ.)
On the type of the von Neumann algebra of an open subgroup of the Neretin group
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Masahiko Yoshinaga (Osaka University)
Milnor fibers of hyperplane arrangements (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Masahiko Yoshinaga (Osaka University)
Milnor fibers of hyperplane arrangements (JAPANESE)
[ Abstract ]
A (central) hyperplane arrangement is a union of finitely many hyperplanes in a linear space. There are many relationships between the intersection lattice of the arrangement and geometry of related spaces. In this talk, we focus on the Milnor fiber of a hyperplane arrangement. The first Betti number of the Milnor fiber is expected to be determined by the combinatorial structure of the intersection lattice, however, it is still open. We discuss two results on the problem. The first (discouraging) one is concerning the dimension of (-1)-eigenspace of the monodromy action on the first cohomology group. We show that it is related to 2-torsions in the first homology of double covering of the (projectivized) complement (j.w. Ishibashi and Sugawara). The second (encouraging) one is related to the Aomoto complex, which is defined in purely combinatorial way. We show that a q-analogue of Aomoto complex determines all nontrivial monodromy eigenspaces of the Milnor fiber.
[ Reference URL ]A (central) hyperplane arrangement is a union of finitely many hyperplanes in a linear space. There are many relationships between the intersection lattice of the arrangement and geometry of related spaces. In this talk, we focus on the Milnor fiber of a hyperplane arrangement. The first Betti number of the Milnor fiber is expected to be determined by the combinatorial structure of the intersection lattice, however, it is still open. We discuss two results on the problem. The first (discouraging) one is concerning the dimension of (-1)-eigenspace of the monodromy action on the first cohomology group. We show that it is related to 2-torsions in the first homology of double covering of the (projectivized) complement (j.w. Ishibashi and Sugawara). The second (encouraging) one is related to the Aomoto complex, which is defined in purely combinatorial way. We show that a q-analogue of Aomoto complex determines all nontrivial monodromy eigenspaces of the Milnor fiber.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022/11/03
Lectures
11:00-12:30 Online
Seminars by Professor O. Emanouilov (Colorado State Univ.)
Professor O. Emanouilov (Colorado State Univ.)
Inverse problems for partial differential equations: past and future works (English)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/88649482949?pwd=Yk9sNzJDNmNmZlRDeXAvcFFtcUkzUT09
Seminars by Professor O. Emanouilov (Colorado State Univ.)
Professor O. Emanouilov (Colorado State Univ.)
Inverse problems for partial differential equations: past and future works (English)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/88649482949?pwd=Yk9sNzJDNmNmZlRDeXAvcFFtcUkzUT09
2022/11/02
Number Theory Seminar
17:00-18:00 Hybrid
Laurent Fargues (Mathematics Institute of Jussieu–Paris Rive Gauche, University of Tokyo)
Some compact generators of D_{lis} (Bun_G,\Lambda) (English)
Laurent Fargues (Mathematics Institute of Jussieu–Paris Rive Gauche, University of Tokyo)
Some compact generators of D_{lis} (Bun_G,\Lambda) (English)
[ Abstract ]
I will speak about some aspect of my joint work with Scholze on the geomerization of the local Langlands correspondence. More precisely, I will explain how to construct explicitly some compact generators of the derived category of étale sheaves on Bun_G, the Artin v-stack of G-bundles on the curve. Those compact generators generalize the classical compactly induced representations in the classical local Langlands program. For this we construct some particular charts on Bun_G and this will be the occasion to review some geometric constructions in our joint work.
I will speak about some aspect of my joint work with Scholze on the geomerization of the local Langlands correspondence. More precisely, I will explain how to construct explicitly some compact generators of the derived category of étale sheaves on Bun_G, the Artin v-stack of G-bundles on the curve. Those compact generators generalize the classical compactly induced representations in the classical local Langlands program. For this we construct some particular charts on Bun_G and this will be the occasion to review some geometric constructions in our joint work.
2022/11/01
Operator Algebra Seminars
16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Hiroki Ishikura (Univ. Tokyo)
Permutation stability of finitely generated free metabelian groups
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Hiroki Ishikura (Univ. Tokyo)
Permutation stability of finitely generated free metabelian groups
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Minkyu Kim (The Univesity of Tokyo)
An obstruction problem associated with finite path-integral (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Minkyu Kim (The Univesity of Tokyo)
An obstruction problem associated with finite path-integral (JAPANESE)
[ Abstract ]
Finite path-integral introduced by Dijkgraaf and Witten in 1990 is a mathematical methodology to construct an Atiyah-Segal type TQFT from finite gauge theory. In three dimensions, it is generalized to Hopf algebra gauge theory of Meusburger, and the corresponding TQFT is known as Turaev-Viro model. On the one hand, the bicommutative Hopf algebra gauge theory is covered by homological algebra. In this talk, we will explain an obstruction problem associated with a refined finite path-integral construction of TQFT's from homological algebra. This talk is based on our study of a folklore claim in condensed matter physics that gapped lattice quantum system, e.g. toric code, is approximated by topological field theories in low temperature.
[ Reference URL ]Finite path-integral introduced by Dijkgraaf and Witten in 1990 is a mathematical methodology to construct an Atiyah-Segal type TQFT from finite gauge theory. In three dimensions, it is generalized to Hopf algebra gauge theory of Meusburger, and the corresponding TQFT is known as Turaev-Viro model. On the one hand, the bicommutative Hopf algebra gauge theory is covered by homological algebra. In this talk, we will explain an obstruction problem associated with a refined finite path-integral construction of TQFT's from homological algebra. This talk is based on our study of a folklore claim in condensed matter physics that gapped lattice quantum system, e.g. toric code, is approximated by topological field theories in low temperature.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Algebraic Geometry Seminar
10:30-12:00 Room #ハイブリッド開催/002 (Graduate School of Math. Sci. Bldg.)
Tatsuro Kawakami (Kyoto)
Extendability of differential forms via Cartier operators (Japanese)
Tatsuro Kawakami (Kyoto)
Extendability of differential forms via Cartier operators (Japanese)
[ Abstract ]
For a normal variety X, we say X satisfies the extension theorem if, for every proper birational morphism from Y, every differential form on the regular locus of X extends to Y. This is a basic property relating differential forms and singularities, and many results are known over the field of complex numbers.
In this talk, we discuss the extension theorem in positive characteristic. Existing studies depend on geometric tools such as log resolutions, (mixed) Hodge theory, the minimal model program, and vanishing theorems, which are not expected to be true or are not known for higher-dimensional varieties in positive characteristic.
For this reason, I introduce a new algebraic approach to the extension theorem using Cartier operators. I also talk about an application of the theory of quasi-F-splitting, which is studied in joint work with Takamatsu-Tanaka-Witaszek-Yobuko-Yoshikawa, to the extension problem.
For a normal variety X, we say X satisfies the extension theorem if, for every proper birational morphism from Y, every differential form on the regular locus of X extends to Y. This is a basic property relating differential forms and singularities, and many results are known over the field of complex numbers.
In this talk, we discuss the extension theorem in positive characteristic. Existing studies depend on geometric tools such as log resolutions, (mixed) Hodge theory, the minimal model program, and vanishing theorems, which are not expected to be true or are not known for higher-dimensional varieties in positive characteristic.
For this reason, I introduce a new algebraic approach to the extension theorem using Cartier operators. I also talk about an application of the theory of quasi-F-splitting, which is studied in joint work with Takamatsu-Tanaka-Witaszek-Yobuko-Yoshikawa, to the extension problem.
2022/10/31
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Eiji Inoue (RIKEN)
The non-archimedean μ-entropy in toric case (Japanese)
https://forms.gle/hYT2hVhDE3q1wDSh6
Eiji Inoue (RIKEN)
The non-archimedean μ-entropy in toric case (Japanese)
[ Abstract ]
The non-archimedean μ-entropy is a functional on the space of test configurations of a polarized variety. It plays a key role in μK-stability and can be interpreted as a dual functional to Perelman’s μ-entropy for Kahler metrics. The fundamental question on the non-archimedean μ-entropy is the existence and uniqueness of maximizers. To find its maximizers, it is natural to extend the functional to a suitable completion of the space of test configurations. For general polarized variety, we can realize such completion and extension based on the non-archimedean pluripotential theory.
In the toric case, the torus invariant subspace of the completion is identified with a suitable space of convex functions on the moment polytope and then the non-archimedean μ-entropy is simply expressed by integrations of convex functions on the polytope. I will show a compactness result in the toric case, by which we conclude the existence of maximizers for the toric non-archimedean μ-entropy.
[ Reference URL ]The non-archimedean μ-entropy is a functional on the space of test configurations of a polarized variety. It plays a key role in μK-stability and can be interpreted as a dual functional to Perelman’s μ-entropy for Kahler metrics. The fundamental question on the non-archimedean μ-entropy is the existence and uniqueness of maximizers. To find its maximizers, it is natural to extend the functional to a suitable completion of the space of test configurations. For general polarized variety, we can realize such completion and extension based on the non-archimedean pluripotential theory.
In the toric case, the torus invariant subspace of the completion is identified with a suitable space of convex functions on the moment polytope and then the non-archimedean μ-entropy is simply expressed by integrations of convex functions on the polytope. I will show a compactness result in the toric case, by which we conclude the existence of maximizers for the toric non-archimedean μ-entropy.
https://forms.gle/hYT2hVhDE3q1wDSh6
2022/10/27
Information Mathematics Seminar
16:50-18:20 Room #123 (Graduate School of Math. Sci. Bldg.)
Katsuyuki Takashima (Waseda Univ.)
Recent Progress in Post-Quantum Cryptography (Japanese)
Katsuyuki Takashima (Waseda Univ.)
Recent Progress in Post-Quantum Cryptography (Japanese)
[ Abstract ]
I will explain recent progress in post-quantum cryptography, particularly, in lattice cryptography.
I will explain recent progress in post-quantum cryptography, particularly, in lattice cryptography.
Lectures
11:00-12:30 Online
Seminars by Professor O. Emanouilov (Colorado State Univ.)
Professor O. Emanouilov (Colorado State Univ.)
Inverse problems for partial differential equations: past and future works (English)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/88649482949?pwd=Yk9sNzJDNmNmZlRDeXAvcFFtcUkzUT09
Seminars by Professor O. Emanouilov (Colorado State Univ.)
Professor O. Emanouilov (Colorado State Univ.)
Inverse problems for partial differential equations: past and future works (English)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/88649482949?pwd=Yk9sNzJDNmNmZlRDeXAvcFFtcUkzUT09
2022/10/25
Algebraic Geometry Seminar
10:30-11:45 Room #ハイブリッド開催/002 (Graduate School of Math. Sci. Bldg.)
Atsushi Ito (Okayama)
Projective normality of general polarized abelian varieties (Japanese)
Atsushi Ito (Okayama)
Projective normality of general polarized abelian varieties (Japanese)
[ Abstract ]
Projective normality is an important property of polarized varieties. Hwang and To prove that a general polarized abelian variety $(X,L)$ of dimension $g$ is projectively normal if $\chi(X,L) \geq (8g)^g/2g!$. In this talk, I will explain that their bound can be weaken as $\chi(X,L) > 2^{2g-1}$, which is sharp. A key tool in the proof is an invariant introduced by Jiang and Pareschi, which measures the basepoint freeness of $\mathbb{Q}$-divisors on abelian varieties.
Projective normality is an important property of polarized varieties. Hwang and To prove that a general polarized abelian variety $(X,L)$ of dimension $g$ is projectively normal if $\chi(X,L) \geq (8g)^g/2g!$. In this talk, I will explain that their bound can be weaken as $\chi(X,L) > 2^{2g-1}$, which is sharp. A key tool in the proof is an invariant introduced by Jiang and Pareschi, which measures the basepoint freeness of $\mathbb{Q}$-divisors on abelian varieties.
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Noboru Ogawa (Tokai University)
Stabilized convex symplectic manifolds are Weinstein (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Noboru Ogawa (Tokai University)
Stabilized convex symplectic manifolds are Weinstein (JAPANESE)
[ Abstract ]
There are two important classes of convexity in symplectic geometry: Liouville and Weinstein structures. Basic objects such as cotangent bundles and Stein manifolds have these structures. In 90s, Eliashberg and Gromov formulated them as symplectic counterparts of Stein manifolds, since then, they have played a significant role in the study of symplectic topology. By definition, a Weinstein structure is a Liouville structure, but the converse is not true in general; McDuff gave the first example which is a Liouville manifold without any Weinstein structures. The purpose of this talk is to present the recent advances on the difference of both structures, up to homotopy. In particular, I will show that the stabilization of the McDuff’s example admits a flexible Weinstein structure. The main part is based on a joint work with Yakov Eliashberg (Stanford University) and Toru Yoshiyasu (Kyoto University of Education). If time permits, I would like to discuss some open questions and progress.
[ Reference URL ]There are two important classes of convexity in symplectic geometry: Liouville and Weinstein structures. Basic objects such as cotangent bundles and Stein manifolds have these structures. In 90s, Eliashberg and Gromov formulated them as symplectic counterparts of Stein manifolds, since then, they have played a significant role in the study of symplectic topology. By definition, a Weinstein structure is a Liouville structure, but the converse is not true in general; McDuff gave the first example which is a Liouville manifold without any Weinstein structures. The purpose of this talk is to present the recent advances on the difference of both structures, up to homotopy. In particular, I will show that the stabilization of the McDuff’s example admits a flexible Weinstein structure. The main part is based on a joint work with Yakov Eliashberg (Stanford University) and Toru Yoshiyasu (Kyoto University of Education). If time permits, I would like to discuss some open questions and progress.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022/10/24
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Taro Fujisawa (Tokyo Denki University)
A new approach to the nilpotent orbit theorem via the $L^2$ extension theorem of Ohsawa-Takegoshi type (Japanese)
https://forms.gle/hYT2hVhDE3q1wDSh6
Taro Fujisawa (Tokyo Denki University)
A new approach to the nilpotent orbit theorem via the $L^2$ extension theorem of Ohsawa-Takegoshi type (Japanese)
[ Abstract ]
I will talk about a new proof of (a part of) the nilpotent orbit theorem for unipotent variations of Hodge structure. This approach is largely inspired by the recent works of Deng and of Sabbah-Schnell. In my proof, the $L^2$ extension theorem of Ohsawa-Takegoshi type plays essential roles.
[ Reference URL ]I will talk about a new proof of (a part of) the nilpotent orbit theorem for unipotent variations of Hodge structure. This approach is largely inspired by the recent works of Deng and of Sabbah-Schnell. In my proof, the $L^2$ extension theorem of Ohsawa-Takegoshi type plays essential roles.
https://forms.gle/hYT2hVhDE3q1wDSh6
2022/10/21
Colloquium
15:30-16:30 Room #オンライン (Graduate School of Math. Sci. Bldg.)
If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.
Neal Bez (Graduate School of Science and Engineering, Saitama University)
The Fourier restriction conjecture (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZcudO-srjMvHtUzVhQQZF9JhDSvy-Oxu2j2
If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.
Neal Bez (Graduate School of Science and Engineering, Saitama University)
The Fourier restriction conjecture (English)
[ Abstract ]
The Fourier restriction conjecture is a central problem in modern harmonic analysis which traces back to deep observations of Elias M. Stein in the 1960s. The conjecture enjoys some remarkable connections to areas such as geometric measure theory, PDE, and number theory. In this talk, I will introduce the conjecture and discuss a few of these connections.
[ Reference URL ]The Fourier restriction conjecture is a central problem in modern harmonic analysis which traces back to deep observations of Elias M. Stein in the 1960s. The conjecture enjoys some remarkable connections to areas such as geometric measure theory, PDE, and number theory. In this talk, I will introduce the conjecture and discuss a few of these connections.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZcudO-srjMvHtUzVhQQZF9JhDSvy-Oxu2j2
Seminar on Probability and Statistics
①14:30-15:40- ②16:20-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Estate Khmaladze (Victoria University of Wellington)
On the theory of distribution free testing of statistical hypothesis
①Empirical processes for discrete and continuous observations: structure, difficulties and resolution.
②Further testing problems: parametric regression and Markov chains. (ENGLISH)
https://docs.google.com/forms/d/e/1FAIpQLScxh_wNRs3WbMUG4S3cGlGAu1ZkP4trLbc08CBrvUDO66hwNg/viewform?usp=sf_link
Estate Khmaladze (Victoria University of Wellington)
On the theory of distribution free testing of statistical hypothesis
①Empirical processes for discrete and continuous observations: structure, difficulties and resolution.
②Further testing problems: parametric regression and Markov chains. (ENGLISH)
[ Abstract ]
The concept of distribution free testing is familiar to all. Everybody, who heard about rank statistics, knows that the distribution of ranks is independent from the distribution of underlying random variables, provided this later is a continuous distribution on the real line. Everybody, who ever used classical goodness of fit tests like Kolmogorov - Smirnov test or Cram\'er-von Mises test, knows that the distribution of statistics of these tests is independent from the distribution of the underlying random variables, again, provided this distribution is a continuous distribution on the real line.
Development in subsequent decades revealed many cracks in existing theory and difficulties in extending the concept of distribution free testing to majority of interesting models. It gradually became clear that the new starting point is needed to expand the theory to these models.
In our lectures we first describe the current situation in empirical and related processes. Then we describe how the new approaches have been developed and what progress has been made.
Then we hope to show how the new approach can be naturally extended to the domain of stochastic processes, and how the important probabilistic models of the processes can be tested in distribution free way. In discrete time, results for Markov chains have been published in 2021. Extension to continuous time will be explored during the current visit to University of Tokyo.
[ Reference URL ]The concept of distribution free testing is familiar to all. Everybody, who heard about rank statistics, knows that the distribution of ranks is independent from the distribution of underlying random variables, provided this later is a continuous distribution on the real line. Everybody, who ever used classical goodness of fit tests like Kolmogorov - Smirnov test or Cram\'er-von Mises test, knows that the distribution of statistics of these tests is independent from the distribution of the underlying random variables, again, provided this distribution is a continuous distribution on the real line.
Development in subsequent decades revealed many cracks in existing theory and difficulties in extending the concept of distribution free testing to majority of interesting models. It gradually became clear that the new starting point is needed to expand the theory to these models.
In our lectures we first describe the current situation in empirical and related processes. Then we describe how the new approaches have been developed and what progress has been made.
Then we hope to show how the new approach can be naturally extended to the domain of stochastic processes, and how the important probabilistic models of the processes can be tested in distribution free way. In discrete time, results for Markov chains have been published in 2021. Extension to continuous time will be explored during the current visit to University of Tokyo.
https://docs.google.com/forms/d/e/1FAIpQLScxh_wNRs3WbMUG4S3cGlGAu1ZkP4trLbc08CBrvUDO66hwNg/viewform?usp=sf_link
2022/10/20
Tokyo-Nagoya Algebra Seminar
16:40-18:10 Online
Please see the reference URL for details on the online seminar.
Martin Kalck (Freiburg University)
A surface and a threefold with equivalent singularity categories (English)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the reference URL for details on the online seminar.
Martin Kalck (Freiburg University)
A surface and a threefold with equivalent singularity categories (English)
[ Abstract ]
We discuss a triangle equivalence between singularity categories of an
affine surface and an affine threefold.
Both are isolated cyclic quotient singularities.
This seems to be the first (non-trivial) example of a singular
equivalence involving varieties of even and odd Krull dimension.
The same approach recovers a result of Dong Yang showing a singular
equivalence between certain cyclic quotient singularities in dimension
2 and certain finite dimensional commutative algebras.
This talk is based on https://arxiv.org/pdf/2103.06584.pdf
[ Reference URL ]We discuss a triangle equivalence between singularity categories of an
affine surface and an affine threefold.
Both are isolated cyclic quotient singularities.
This seems to be the first (non-trivial) example of a singular
equivalence involving varieties of even and odd Krull dimension.
The same approach recovers a result of Dong Yang showing a singular
equivalence between certain cyclic quotient singularities in dimension
2 and certain finite dimensional commutative algebras.
This talk is based on https://arxiv.org/pdf/2103.06584.pdf
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2022/10/19
Seminar on Probability and Statistics
10:30-11:40 Room # (Graduate School of Math. Sci. Bldg.)
Hayate Yamagishi (Graduate School of Mathematical Sciences, The University of Tokyo)
https://docs.google.com/forms/d/e/1FAIpQLSd3i_gFci4Dc8T8gjtMigm08aIoQH6gM_Yfw0bHfppM1CNmag/viewform?usp=sf_link
Hayate Yamagishi (Graduate School of Mathematical Sciences, The University of Tokyo)
[ Abstract ]
[ Reference URL ]https://docs.google.com/forms/d/e/1FAIpQLSd3i_gFci4Dc8T8gjtMigm08aIoQH6gM_Yfw0bHfppM1CNmag/viewform?usp=sf_link
Lectures
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
If you wish to participate online, please register by 17:00 on the 18th from the reference URL.
Mykhaylo Shkolnikov (Princeton University)
Probabilistic solutions of singular free boundary problems (English)
https://forms.gle/XXH2cAb18pQhC6w96
If you wish to participate online, please register by 17:00 on the 18th from the reference URL.
Mykhaylo Shkolnikov (Princeton University)
Probabilistic solutions of singular free boundary problems (English)
[ Abstract ]
The main focus of the talk will be on a new, probabilistic, concept of solution to singular free boundary problems, in which boundary points may move at infinite speed. I will discuss this new concept in the context of Stefan problems from mathematical physics that describe melting/solidification of a solid/liquid (e.g., ice/water) in the presence of supercooling. In particular, I will present new global existence, regularity and uniqueness results for the two geometrically simplest settings: flat and radial. Based on joint works with Sergey Nadtochiy, Francois Delarue and Yucheng Guo.
[ Reference URL ]The main focus of the talk will be on a new, probabilistic, concept of solution to singular free boundary problems, in which boundary points may move at infinite speed. I will discuss this new concept in the context of Stefan problems from mathematical physics that describe melting/solidification of a solid/liquid (e.g., ice/water) in the presence of supercooling. In particular, I will present new global existence, regularity and uniqueness results for the two geometrically simplest settings: flat and radial. Based on joint works with Sergey Nadtochiy, Francois Delarue and Yucheng Guo.
https://forms.gle/XXH2cAb18pQhC6w96
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