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Seminar information archive
Seminar information archive ～04/25｜Today's seminar 04/26 | Future seminars 04/27～
2022/11/24
Applied Analysis
16:00-17:30 Room #370 (Graduate School of Math. Sci. Bldg.)
Kyohei Itakura (The University of Tokyo)
Strong radiation condition and stationary scattering theory for 1-body Stark operators (Japanese)
[ Reference URL ]
https://forms.gle/admRaVnmPjFyp5op9
Kyohei Itakura (The University of Tokyo)
Strong radiation condition and stationary scattering theory for 1-body Stark operators (Japanese)
[ Reference URL ]
https://forms.gle/admRaVnmPjFyp5op9
Information Mathematics Seminar
16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)
Masaya Yasuda (Rikkyo Univ.)
Attacks for lattice problems assuring the security of lattice-based cryptography (Japanese)
Masaya Yasuda (Rikkyo Univ.)
Attacks for lattice problems assuring the security of lattice-based cryptography (Japanese)
[ Abstract ]
Lattice-based cryptography is one of post-quantum cryptography, and it is useful for construction of high-functional encryption such as fully homomorphic encryption. In this talk, I introduce methods to attack lattice problems assuring the security of lattice based cryptography. Specifically, I present algorithms of lattice basis reduction such as LLL and BKZ that are required for solving lattice problems. I also describe how to apply reduction algorithms to attacking LWE and NTRU problems.
Lattice-based cryptography is one of post-quantum cryptography, and it is useful for construction of high-functional encryption such as fully homomorphic encryption. In this talk, I introduce methods to attack lattice problems assuring the security of lattice based cryptography. Specifically, I present algorithms of lattice basis reduction such as LLL and BKZ that are required for solving lattice problems. I also describe how to apply reduction algorithms to attacking LWE and NTRU problems.
2022/11/22
Algebraic Geometry Seminar
10:30-12:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Sho Tanimoto (Nagoya)
Non-free sections of Fano fibrations (日本語)
Sho Tanimoto (Nagoya)
Non-free sections of Fano fibrations (日本語)
[ Abstract ]
Manin’s Conjecture predicts the asymptotic formula for the counting function of rational points over number fields or global function fields. In the late 80’s, Batyrev developed a heuristic argument for Manin’s Conjecture over global function fields, and the assumptions underlying Batyrev’s heuristics are refined and formulated as Geometric Manin’s Conjecture. Geometric Manin’s Conjecture is a set of conjectures regarding properties of the space of sections of Fano fibrations, and it consists of three conjectures: (i) Pathological components are controlled by Fujita invariants; (ii) For each nef algebraic class, a non-pathological component which should be counted in Manin’s Conjecture is unique (This component is called as Manin components); (iii) Manin components exhibit homological or motivic stability. In this talk we discuss our proofs of GMC (i) over complex numbers using theory of foliations and the minimal model program. Using this result, we prove that these pathological components are coming from a bounded family of accumulating maps. This is joint work in progress with Brian Lehmann and Eric Riedl.
Manin’s Conjecture predicts the asymptotic formula for the counting function of rational points over number fields or global function fields. In the late 80’s, Batyrev developed a heuristic argument for Manin’s Conjecture over global function fields, and the assumptions underlying Batyrev’s heuristics are refined and formulated as Geometric Manin’s Conjecture. Geometric Manin’s Conjecture is a set of conjectures regarding properties of the space of sections of Fano fibrations, and it consists of three conjectures: (i) Pathological components are controlled by Fujita invariants; (ii) For each nef algebraic class, a non-pathological component which should be counted in Manin’s Conjecture is unique (This component is called as Manin components); (iii) Manin components exhibit homological or motivic stability. In this talk we discuss our proofs of GMC (i) over complex numbers using theory of foliations and the minimal model program. Using this result, we prove that these pathological components are coming from a bounded family of accumulating maps. This is joint work in progress with Brian Lehmann and Eric Riedl.
Operator Algebra Seminars
16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Ryosuke Sato (Chuo Univ.)
Multiplicative characters and Gaussian fluctuation limits
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Ryosuke Sato (Chuo Univ.)
Multiplicative characters and Gaussian fluctuation limits
[ 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.
Teruaki Kitano (Soka University)
Epimorphism between knot groups and isomorphisms on character varieties (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Teruaki Kitano (Soka University)
Epimorphism between knot groups and isomorphisms on character varieties (JAPANESE)
[ Abstract ]
A partial order on the set of prime knots is given by the existence of an epimorphism between the fundamental groups of the knot complements. In this talk we will survey some basic properties of this order, and discuss some results and questions in connection with the SL(2,C)-character variety. In particular we study to what extend the SL(2,C)-character variety to determine the knot. This talk will be based on joint works with Michel Boileau(Univ. Aix-Marseille), Steven Sivek(Imperial College London), and Raphael Zentner(Univ. Regensburg).
[ Reference URL ]A partial order on the set of prime knots is given by the existence of an epimorphism between the fundamental groups of the knot complements. In this talk we will survey some basic properties of this order, and discuss some results and questions in connection with the SL(2,C)-character variety. In particular we study to what extend the SL(2,C)-character variety to determine the knot. This talk will be based on joint works with Michel Boileau(Univ. Aix-Marseille), Steven Sivek(Imperial College London), and Raphael Zentner(Univ. Regensburg).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022/11/21
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Joe Kamimoto (Kyushu University)
Resolution of singularities for $C^{\infty}$ functions and meromorphy of local zeta functions (Japanese)
https://forms.gle/hYT2hVhDE3q1wDSh6
Joe Kamimoto (Kyushu University)
Resolution of singularities for $C^{\infty}$ functions and meromorphy of local zeta functions (Japanese)
[ Abstract ]
In this talk, we attempt to resolve the singularities of the zero variety of a $C^{\infty}$ function of two variables as much as possible by using ordinary blowings up. As a result, we formulate an algorithm to locally express the zero variety in the “almost” normal crossings form, which is close to the normal crossings form but may include flat functions. As an application, we investigate analytic continuation of local zeta functions associated with $C^{\infty}$ functions of two variables.
[ Reference URL ]In this talk, we attempt to resolve the singularities of the zero variety of a $C^{\infty}$ function of two variables as much as possible by using ordinary blowings up. As a result, we formulate an algorithm to locally express the zero variety in the “almost” normal crossings form, which is close to the normal crossings form but may include flat functions. As an application, we investigate analytic continuation of local zeta functions associated with $C^{\infty}$ functions of two variables.
https://forms.gle/hYT2hVhDE3q1wDSh6
2022/11/17
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
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.
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