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Seminar information archive
Seminar information archive ～01/23｜Today's seminar 01/24 | Future seminars 01/25～
2024/11/25
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.
Leon Frober (Grand Valley State University)
Free energy and ground state of the spiked SSK spin-glass model
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Leon Frober (Grand Valley State University)
Free energy and ground state of the spiked SSK spin-glass model
[ Abstract ]
Spin-glasses are essentially mathematical models of particle interactions, and were originally describing magnetic states characterized by randomness in condensed matter physics. Due to the versatility of these types of models, however, they are now studied much more broadly for various complex systems such as statistical inference problems, weather/climate models or even neural networks. In this talk we will lay out the basic concepts of spin-glass models, while then focusing on the spiked SSK variant and its free energy as well as ground state energy. Furthermore we will discuss how one can determine these quantities including their lower order fluctuations with a so called "TAP approach" that was in this comprehensive form introduced in 2016 by N. Kistler and D. Belius, and what its benefits are compared to the earlier established "Parisi approach".
Spin-glasses are essentially mathematical models of particle interactions, and were originally describing magnetic states characterized by randomness in condensed matter physics. Due to the versatility of these types of models, however, they are now studied much more broadly for various complex systems such as statistical inference problems, weather/climate models or even neural networks. In this talk we will lay out the basic concepts of spin-glass models, while then focusing on the spiked SSK variant and its free energy as well as ground state energy. Furthermore we will discuss how one can determine these quantities including their lower order fluctuations with a so called "TAP approach" that was in this comprehensive form introduced in 2016 by N. Kistler and D. Belius, and what its benefits are compared to the earlier established "Parisi approach".
2024/11/22
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Hiroshi Iritani (Kyoto University)
Quantum cohomology of blowups
Hiroshi Iritani (Kyoto University)
Quantum cohomology of blowups
[ Abstract ]
I will discuss a decomposition theorem for the quantum cohomology of a smooth projective variety blown up along a smooth subvariety. I will start with a general relationship between decomposition of quantum cohomology and extremal contractions, and then specialize to the case of blowups. Applications to birational geometry of this result have been announced by Katzarkov, Kontsevich, Pantev and Yu.
I will discuss a decomposition theorem for the quantum cohomology of a smooth projective variety blown up along a smooth subvariety. I will start with a general relationship between decomposition of quantum cohomology and extremal contractions, and then specialize to the case of blowups. Applications to birational geometry of this result have been announced by Katzarkov, Kontsevich, Pantev and Yu.
2024/11/19
Operator Algebra Seminars
16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)
Ryosuke Sato (Chuo Univ.)
The quantum de Finetti theorem and operator-valued Martin boundaries
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Ryosuke Sato (Chuo Univ.)
The quantum de Finetti theorem and operator-valued Martin boundaries
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Operator Algebra Seminars
15:00-16:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Roozbeh Hazrat (Western Sydney University)
Monoids, Dynamics and Leavitt path algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Roozbeh Hazrat (Western Sydney University)
Monoids, Dynamics and Leavitt path algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Bruno Scárdua (Federal University of Rio de Janeiro)
On real center singularities of complex vector fields on surfaces (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Bruno Scárdua (Federal University of Rio de Janeiro)
On real center singularities of complex vector fields on surfaces (ENGLISH)
[ Abstract ]
One of the various versions of the classical Lyapunov-Poincaré center theorem states that a nondegenerate real analytic center type planar vector field singularity admits an analytic first integral. In a more proof of this result, R. Moussu establishes important connection between this result and the theory of singularities of holomorphic foliations ([2]). In this paper we consider generalizations for two main frameworks: (i) planar real analytic vector fields with "many" periodic orbits near the singularity and
(ii) germs of holomorphic foliations having a suitable singularity in dimension two.
In this talk we discuss some versions of Poincaré-Lyapunov center theorem, including for the case of holomorphic vector fields. We also give some applications, hinting that there is much more to be explored in this framework.
References
[1] V. León, B. Scárdua, On a Theorem of Lyapunov-Poincaré in Higher Dimensions, July 2021, Arnold Mathematical Journal 7(3) DOI:10.1007/s40598-021-00183-x.
[2] R. Moussu: Une démonstration géométrique d’un théorème de Lyapunov-Poincaré. Astérisque, tome 98-99 (1982), p. 216-223.
[3] A. Lyapunov: Etude d’un cas particulier du problème de la stabilité du mouvement. Mat. Sbornik 17 (1893) pages 252-333 (Russe).
[4] H. Poincaré: Mémoire sur les courbes définies par une équation différentielle (I), Journal de mathématiques pures et appliquées 3e série, tome 7 (1881), p. 375-422.
[5] Minoru Urabe and Yasutaka Sibuya; On Center of Higher Dimensions; Journal of Science of the Hiroshima University, Ser. A, . Vol. 19, No. I, July, 1955.
[ Reference URL ]One of the various versions of the classical Lyapunov-Poincaré center theorem states that a nondegenerate real analytic center type planar vector field singularity admits an analytic first integral. In a more proof of this result, R. Moussu establishes important connection between this result and the theory of singularities of holomorphic foliations ([2]). In this paper we consider generalizations for two main frameworks: (i) planar real analytic vector fields with "many" periodic orbits near the singularity and
(ii) germs of holomorphic foliations having a suitable singularity in dimension two.
In this talk we discuss some versions of Poincaré-Lyapunov center theorem, including for the case of holomorphic vector fields. We also give some applications, hinting that there is much more to be explored in this framework.
References
[1] V. León, B. Scárdua, On a Theorem of Lyapunov-Poincaré in Higher Dimensions, July 2021, Arnold Mathematical Journal 7(3) DOI:10.1007/s40598-021-00183-x.
[2] R. Moussu: Une démonstration géométrique d’un théorème de Lyapunov-Poincaré. Astérisque, tome 98-99 (1982), p. 216-223.
[3] A. Lyapunov: Etude d’un cas particulier du problème de la stabilité du mouvement. Mat. Sbornik 17 (1893) pages 252-333 (Russe).
[4] H. Poincaré: Mémoire sur les courbes définies par une équation différentielle (I), Journal de mathématiques pures et appliquées 3e série, tome 7 (1881), p. 375-422.
[5] Minoru Urabe and Yasutaka Sibuya; On Center of Higher Dimensions; Journal of Science of the Hiroshima University, Ser. A, . Vol. 19, No. I, July, 1955.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/11/18
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yusaku Tiba (Ochanomizu Univ.)
Polarizations and convergences of holomorphic sections on the tangent bundle of a Bohr-Sommerfeld Lagrangian submanifold (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yusaku Tiba (Ochanomizu Univ.)
Polarizations and convergences of holomorphic sections on the tangent bundle of a Bohr-Sommerfeld Lagrangian submanifold (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/11/15
Colloquium
15:30-16:30 Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Michael Pevzner (University of Reims / CNRS / The University of Tokyo)
Symmetry breaking for branching problems (ENGLISH)
https://forms.gle/DcsJVYS4fvMLfPEM8
Michael Pevzner (University of Reims / CNRS / The University of Tokyo)
Symmetry breaking for branching problems (ENGLISH)
[ Abstract ]
Restricting a group representation to its subgroups is a fundamental issue in Representation Theory. This process involves exploring how large symmetries can be broken down into smaller symmetries. Known as the branching problem, it provides a unifying framework for various seemingly disparate topics, including fusion rules, Clebsch-Gordan coefficients, Pieri rules for integral partitions, Plancherel-type formulas, Theta correspondence, and more recently, the Gross-Prasad-Gan conjectures.
Beyond analyzing abstract branching rules, constructing explicit operators that implement this symmetry breaking in concrete geometric models of infinite-dimensional representations of real reductive groups is a compelling and challenging problem. This field, located at the intersection of global analysis, Lie Theory, the geometry of homogeneous spaces, and algebraic representation theory, has attracted significant attention over the past decade. We will illustrate these concepts with key examples and provide an overview of the guiding principles that are shaping the emerging theory of symmetry breaking operators, along with original ideas related to holographic transforms and the associated generating operators.
[ Reference URL ]Restricting a group representation to its subgroups is a fundamental issue in Representation Theory. This process involves exploring how large symmetries can be broken down into smaller symmetries. Known as the branching problem, it provides a unifying framework for various seemingly disparate topics, including fusion rules, Clebsch-Gordan coefficients, Pieri rules for integral partitions, Plancherel-type formulas, Theta correspondence, and more recently, the Gross-Prasad-Gan conjectures.
Beyond analyzing abstract branching rules, constructing explicit operators that implement this symmetry breaking in concrete geometric models of infinite-dimensional representations of real reductive groups is a compelling and challenging problem. This field, located at the intersection of global analysis, Lie Theory, the geometry of homogeneous spaces, and algebraic representation theory, has attracted significant attention over the past decade. We will illustrate these concepts with key examples and provide an overview of the guiding principles that are shaping the emerging theory of symmetry breaking operators, along with original ideas related to holographic transforms and the associated generating operators.
https://forms.gle/DcsJVYS4fvMLfPEM8
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Sho Tanimoto (Nagoya University)
The spaces of rational curves on del Pezzo surfaces via conic bundles
Sho Tanimoto (Nagoya University)
The spaces of rational curves on del Pezzo surfaces via conic bundles
[ Abstract ]
There have been extensive activities on counting functions of rational points of bounded height on del Pezzo surfaces, and one of prominent approaches to this problem is by the usage of conic bundle structures on del Pezzo surfaces. This leads to upper and lower bounds of correct magnitude for quartic del Pezzo surfaces.
In this talk, I will explain how conic bundle structures on del Pezzo surfaces induce fibration structures on the spaces of rational curves on such surfaces. Then I will explain applications of this structure which include:
1. upper bounds of correct magnitude for the counting function of rational curves on quartic del Pezzo surfaces over finite fields.
2. rationality of the space of rational curves on a quartic del Pezzo surface.
Finally, I will explain our ongoing proof of homological stability for the spaces of rational curves on quartic del Pezzo surfaces. This is joint work in progress with Ronno Das, Brian Lehmann, and Philip Tosteson.
There have been extensive activities on counting functions of rational points of bounded height on del Pezzo surfaces, and one of prominent approaches to this problem is by the usage of conic bundle structures on del Pezzo surfaces. This leads to upper and lower bounds of correct magnitude for quartic del Pezzo surfaces.
In this talk, I will explain how conic bundle structures on del Pezzo surfaces induce fibration structures on the spaces of rational curves on such surfaces. Then I will explain applications of this structure which include:
1. upper bounds of correct magnitude for the counting function of rational curves on quartic del Pezzo surfaces over finite fields.
2. rationality of the space of rational curves on a quartic del Pezzo surface.
Finally, I will explain our ongoing proof of homological stability for the spaces of rational curves on quartic del Pezzo surfaces. This is joint work in progress with Ronno Das, Brian Lehmann, and Philip Tosteson.
2024/11/13
Lie Groups and Representation Theory
17:30-18:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Richard Stanley (MIT)
Some combinatorial aspects of cyclotomic polynomials
Richard Stanley (MIT)
Some combinatorial aspects of cyclotomic polynomials
[ Abstract ]
Euler showed that the number of partitions of n into distinct parts is equal to the number of partitions of n into odd parts. MacMahon showed that the number of partitions of n for which no part occurs exactly once is equal to the number of partitions of n into parts divisible by 2 or 3. Both these results are instances of a general phenomenon based on the fact that certain polynomials are the product of cyclotomic polynomials. After discussing this assertion, we explain how it can be extended to such topics as counting certain polynomials over finite fields and obtaining Dirichlet series generating functions for certain classes of integers.
Euler showed that the number of partitions of n into distinct parts is equal to the number of partitions of n into odd parts. MacMahon showed that the number of partitions of n for which no part occurs exactly once is equal to the number of partitions of n into parts divisible by 2 or 3. Both these results are instances of a general phenomenon based on the fact that certain polynomials are the product of cyclotomic polynomials. After discussing this assertion, we explain how it can be extended to such topics as counting certain polynomials over finite fields and obtaining Dirichlet series generating functions for certain classes of integers.
FJ-LMI Seminar
13:30-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Stefano OLLA (Université de Paris Dauphine - PSL Research University)
Diffusive behaviour in extended completely integrable dynamics (英語)
https://fj-lmi.cnrs.fr/seminars/
Stefano OLLA (Université de Paris Dauphine - PSL Research University)
Diffusive behaviour in extended completely integrable dynamics (英語)
[ Abstract ]
On a diffusive space-time scaling, density fluctuations behave very differently in extended completely integrable systems with respect to chaotic systems. I will expose some recent results concerning the one dimensional hard rods infinite dynamics and the box-ball cellular automata (an ultradiscretization of the KdV equation). Joint works with Pablo Ferrari, Makiko Sasada, Hayate Suda.
[ Reference URL ]On a diffusive space-time scaling, density fluctuations behave very differently in extended completely integrable systems with respect to chaotic systems. I will expose some recent results concerning the one dimensional hard rods infinite dynamics and the box-ball cellular automata (an ultradiscretization of the KdV equation). Joint works with Pablo Ferrari, Makiko Sasada, Hayate Suda.
https://fj-lmi.cnrs.fr/seminars/
2024/11/12
Tuesday Seminar on Topology
17:30-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Joint with Lie Groups and Representation Theory Seminar
Junko Inoue (Tottori University)
Holomorphically induced representations of some solvable Lie groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with Lie Groups and Representation Theory Seminar
Junko Inoue (Tottori University)
Holomorphically induced representations of some solvable Lie groups (JAPANESE)
[ Abstract ]
From a viewpoint of the orbit method, holomorphic induction is originally based on the idea of realizing an irreducible unitary representation of a Lie group $G$ in an $L^2$-space of some holomorphic sections of some line bundle over a $G$-homogeneous space associated with a polarization for a linear form of the Lie algebra of $G$. It is a generalization of ordinary induction from a unitary character; Through this process, Auslander-Kostant constructed the irreducible unitary representations of type 1, connected, simply connected solvable Lie groups.
In this talk, focusing on the class of exponential solvable Lie groups, we are concerned with holomorphically induced representations $\rho$ in some general settings.
We would like to discuss the following problems:
(1) conditions of non-vanishing of $\rho$,
(2) decomposition of $\rho$ into a direct integral of irreducible representations,
(3) Frobenius reciprocity in the sense of Penney distributions.
[ Reference URL ]From a viewpoint of the orbit method, holomorphic induction is originally based on the idea of realizing an irreducible unitary representation of a Lie group $G$ in an $L^2$-space of some holomorphic sections of some line bundle over a $G$-homogeneous space associated with a polarization for a linear form of the Lie algebra of $G$. It is a generalization of ordinary induction from a unitary character; Through this process, Auslander-Kostant constructed the irreducible unitary representations of type 1, connected, simply connected solvable Lie groups.
In this talk, focusing on the class of exponential solvable Lie groups, we are concerned with holomorphically induced representations $\rho$ in some general settings.
We would like to discuss the following problems:
(1) conditions of non-vanishing of $\rho$,
(2) decomposition of $\rho$ into a direct integral of irreducible representations,
(3) Frobenius reciprocity in the sense of Penney distributions.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie Groups and Representation Theory
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Joint with Tuesday Seminar on Topology
Junko Inoue (Tottori University)
Holomorphically induced representations of some solvable Lie groups
(Japanese )
Joint with Tuesday Seminar on Topology
Junko Inoue (Tottori University)
Holomorphically induced representations of some solvable Lie groups
(Japanese )
[ Abstract ]
From a viewpoint of the orbit method, holomorphic induction is originally based on the idea of realizing an irreducible unitary representation of a Lie group $G$ in an $L^2$-space of some holomorphic sections of some line bundle over a $G$-homogeneous space associated with a polarization for a linear form of the Lie algebra of $G$. It is a generalization of ordinary induction from a unitary character; Through this process, Auslander-Kostant constructed the irreducible unitary representations of type 1, connected, simply connected solvable Lie groups.
In this talk, focusing on the class of exponential solvable Lie groups, we are concerned with holomorphically induced representations $\rho$ in some general settings.
We would like to discuss the following problems:
(1) conditions of non-vanishing of $\rho$,
(2) decomposition of $\rho$ into a direct integral of irreducible representations,
(3) Frobenius reciprocity in the sense of Penney distributions.
From a viewpoint of the orbit method, holomorphic induction is originally based on the idea of realizing an irreducible unitary representation of a Lie group $G$ in an $L^2$-space of some holomorphic sections of some line bundle over a $G$-homogeneous space associated with a polarization for a linear form of the Lie algebra of $G$. It is a generalization of ordinary induction from a unitary character; Through this process, Auslander-Kostant constructed the irreducible unitary representations of type 1, connected, simply connected solvable Lie groups.
In this talk, focusing on the class of exponential solvable Lie groups, we are concerned with holomorphically induced representations $\rho$ in some general settings.
We would like to discuss the following problems:
(1) conditions of non-vanishing of $\rho$,
(2) decomposition of $\rho$ into a direct integral of irreducible representations,
(3) Frobenius reciprocity in the sense of Penney distributions.
2024/11/11
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takahiro Inayama (Tokyo University of Science)
Singular Nakano positivity of direct image sheaves (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Takahiro Inayama (Tokyo University of Science)
Singular Nakano positivity of direct image sheaves (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/11/06
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Piotr Pstrągowski (Kyoto University)
The even filtration and prismatic cohomology (English)
Piotr Pstrągowski (Kyoto University)
The even filtration and prismatic cohomology (English)
[ Abstract ]
The even filtration, introduced by Hahn-Raksit-Wilson, is a canonical filtration attached to a commutative ring spectrum which measures its failure to be even. Despite its simple definition, the even filtration recovers many arithmetically important constructions, such as the Adams-Novikov filtration of the sphere or the Bhatt-Morrow-Scholze filtration on topological Hochschild homology, showing that they are all invariants of the commutative ring spectrum alone. I will describe a linear variant of the even filtration which is naturally defined on associative rings as well as joint work with Raksit on the resulting extension of prismatic cohomology to the context of E_2-rings.
The even filtration, introduced by Hahn-Raksit-Wilson, is a canonical filtration attached to a commutative ring spectrum which measures its failure to be even. Despite its simple definition, the even filtration recovers many arithmetically important constructions, such as the Adams-Novikov filtration of the sphere or the Bhatt-Morrow-Scholze filtration on topological Hochschild homology, showing that they are all invariants of the commutative ring spectrum alone. I will describe a linear variant of the even filtration which is naturally defined on associative rings as well as joint work with Raksit on the resulting extension of prismatic cohomology to the context of E_2-rings.
Operator Algebra Seminars
15:00-16:30 Room #126 (Graduate School of Math. Sci. Bldg.)
The day of a week, the time and the room are all different from the usual ones.
Colin McSwiggen (Academia Sinica)
The limiting Horn inequalities in infinite dimensions
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
The day of a week, the time and the room are all different from the usual ones.
Colin McSwiggen (Academia Sinica)
The limiting Horn inequalities in infinite dimensions
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2024/11/05
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.
Jun Murakami (Waseda University)
On complexified tetrahedrons associated with the double twist knots and its application to the volume conjecture (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Jun Murakami (Waseda University)
On complexified tetrahedrons associated with the double twist knots and its application to the volume conjecture (JAPANESE)
[ Abstract ]
In this talk, I first would like to explain complexified tetrahedrons which subdivide the complement of a double twist knot, and then talk about their application to the volume conjecture. Complexified tetrahedrons are introduced by using the fundamental group, and they are deformations of the regular ideal octahedron which is a half of the complement of the Borromean rings. Such deformations correspond to the surgeries of the Borromean rings producing the double twist knots.
On the other hand, the colored Jones polynomials of the double twist knots are given by the quantum 6j symbol with some extra terms. We see the correspondence of the quantum 6j symbol and the volume of a complexified terahedron by using the Neumann-Zagier function, and we can apply such correspondence to prove the volume conjecture for the double twist knots. To do this, the ADO invariant is used instead of the colored Jones invariant. The l'Hopital's rule is applied to get the ADO invariant, and integral by parts solves the big cancellation problem. At the last, it is shown that the application of the saddle point method is not so hard for this case.
[ Reference URL ]In this talk, I first would like to explain complexified tetrahedrons which subdivide the complement of a double twist knot, and then talk about their application to the volume conjecture. Complexified tetrahedrons are introduced by using the fundamental group, and they are deformations of the regular ideal octahedron which is a half of the complement of the Borromean rings. Such deformations correspond to the surgeries of the Borromean rings producing the double twist knots.
On the other hand, the colored Jones polynomials of the double twist knots are given by the quantum 6j symbol with some extra terms. We see the correspondence of the quantum 6j symbol and the volume of a complexified terahedron by using the Neumann-Zagier function, and we can apply such correspondence to prove the volume conjecture for the double twist knots. To do this, the ADO invariant is used instead of the colored Jones invariant. The l'Hopital's rule is applied to get the ADO invariant, and integral by parts solves the big cancellation problem. At the last, it is shown that the application of the saddle point method is not so hard for this case.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/11/01
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Gerard van der Geer (University of Amsterdam)
The cycle class of the supersingular locus (English)
Gerard van der Geer (University of Amsterdam)
The cycle class of the supersingular locus (English)
[ Abstract ]
Deuring gave a now classical formula for the number of supersingular elliptic curves
in characteristic p. We generalize this to a formula for the cycle class of the
supersingular locus in the moduli space of principally polarized abelian varieties
of given dimension g in characteristic p. The formula determines the class up to
a multiple and shows that it lies in the tautological ring. We also give the multiple
for g up to 4. This is joint work with S. Harashita.
Deuring gave a now classical formula for the number of supersingular elliptic curves
in characteristic p. We generalize this to a formula for the cycle class of the
supersingular locus in the moduli space of principally polarized abelian varieties
of given dimension g in characteristic p. The formula determines the class up to
a multiple and shows that it lies in the tautological ring. We also give the multiple
for g up to 4. This is joint work with S. Harashita.
FJ-LMI Seminar
14:00-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Thomas GILETTI (Université Clermont-Auvergne)
Propagating behaviour of solutions of multistable reaction-diffusion equations (英語)
https://fj-lmi.cnrs.fr/seminars/
Thomas GILETTI (Université Clermont-Auvergne)
Propagating behaviour of solutions of multistable reaction-diffusion equations (英語)
[ Abstract ]
This talk will be devoted to propagation phenomena for a general scalar reaction-diffusion PDE, when it may admit an arbitrarily large number of stationary states. It is well known that, in some simple cases, special travelling front solutions (depending on a single variable moving with a constant speed) arise in the large time behaviour of solutions. Due to this feature, reaction-diffusion equations have become ubiquituous in the modelling of spatial invasions in ecology, population dynamics and biology. However, in general, large time propagation can no longer be described by a single front, but by a family of several successive fronts (or `propagating terrace') involving intermediate transient equilibria. I will review several methods, including a connection with Sturm-Liouville theory, to handle such dynamics.
[ Reference URL ]This talk will be devoted to propagation phenomena for a general scalar reaction-diffusion PDE, when it may admit an arbitrarily large number of stationary states. It is well known that, in some simple cases, special travelling front solutions (depending on a single variable moving with a constant speed) arise in the large time behaviour of solutions. Due to this feature, reaction-diffusion equations have become ubiquituous in the modelling of spatial invasions in ecology, population dynamics and biology. However, in general, large time propagation can no longer be described by a single front, but by a family of several successive fronts (or `propagating terrace') involving intermediate transient equilibria. I will review several methods, including a connection with Sturm-Liouville theory, to handle such dynamics.
https://fj-lmi.cnrs.fr/seminars/
2024/10/30
Infinite Analysis Seminar Tokyo
15:30-16:30 Room # (Graduate School of Math. Sci. Bldg.)
Shin'ichi Arita (The University of Tokyo)
Dirac作用素に対するRellich型の定理について (日本語)
Shin'ichi Arita (The University of Tokyo)
Dirac作用素に対するRellich型の定理について (日本語)
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Masaya Sato (University of Tokyo)
Representability of Hochschild homology in the category of motives with modulus (日本語)
Masaya Sato (University of Tokyo)
Representability of Hochschild homology in the category of motives with modulus (日本語)
[ Abstract ]
There is a map from algebraic K-theory to Hochschild homology, called a trace map. This map developed the study of algebraic K-theory. Algebraic K-theory is A^1-invariant on the category of smooth schemes over a field, so the Voevodsky’s motivic homotopy theory is a nice way to study algebraic K-theory. However, Hochschild homology is not A^1-invariant, so Voevodsky’s theory doesn’t capture it. In this talk, we will extend Hochschild homology of schemes to modulus pairs, and it is representable in the category of motives with modulus defined by Kahn-Miyazaki-Saito-Yamazaki.
There is a map from algebraic K-theory to Hochschild homology, called a trace map. This map developed the study of algebraic K-theory. Algebraic K-theory is A^1-invariant on the category of smooth schemes over a field, so the Voevodsky’s motivic homotopy theory is a nice way to study algebraic K-theory. However, Hochschild homology is not A^1-invariant, so Voevodsky’s theory doesn’t capture it. In this talk, we will extend Hochschild homology of schemes to modulus pairs, and it is representable in the category of motives with modulus defined by Kahn-Miyazaki-Saito-Yamazaki.
2024/10/29
Operator Algebra Seminars
16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)
Ayumi Ukai (Nagoya Univ.)
On Hastings factorization for quantum many-body systems
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Ayumi Ukai (Nagoya Univ.)
On Hastings factorization for quantum many-body systems
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
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.
Takahito Naito (Nippon Institute of Technology)
Cartan calculus in string topology (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Takahito Naito (Nippon Institute of Technology)
Cartan calculus in string topology (JAPANESE)
[ Abstract ]
The homology of the free loop space of a closed oriented manifold (called the loop homology) has rich algebraic structures. In the theory of string topology due to Chas and Sullivan, it is well known that the loop homology has a structure of Gerstenhabar algebras with a multiplication called the loop product and a Lie bracket called the loop bracket. On the other hand, Kuribayashi, Wakatsuki, Yamaguchi and the speaker gave a Cartan calculus on the loop homology, which is a geometric description of a homotopy Cartan calculus in the sense of Fiorenza and Kowalzig on the Hochschild homology.
In this talk, we will investigate a relationship between the string topology operations and the Cartan calculus. Especially, we will show that the Cartan calculus can be described by using the loop product and the loop bracket with rational coefficients. As an application, the nilpotency of some loop homology classes are determined.
[ Reference URL ]The homology of the free loop space of a closed oriented manifold (called the loop homology) has rich algebraic structures. In the theory of string topology due to Chas and Sullivan, it is well known that the loop homology has a structure of Gerstenhabar algebras with a multiplication called the loop product and a Lie bracket called the loop bracket. On the other hand, Kuribayashi, Wakatsuki, Yamaguchi and the speaker gave a Cartan calculus on the loop homology, which is a geometric description of a homotopy Cartan calculus in the sense of Fiorenza and Kowalzig on the Hochschild homology.
In this talk, we will investigate a relationship between the string topology operations and the Cartan calculus. Especially, we will show that the Cartan calculus can be described by using the loop product and the loop bracket with rational coefficients. As an application, the nilpotency of some loop homology classes are determined.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/10/28
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Matsumoto (Osaka Univ.)
. (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Yoshihiko Matsumoto (Osaka Univ.)
. (Japanese)
[ Abstract ]
.
[ Reference URL ].
https://forms.gle/gTP8qNZwPyQyxjTj8
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.
Kohki Sakamoto (The University of Tokyo)
Harmonic measures in invariant random graphs on Gromov-hyperbolic spaces (日本語)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Kohki Sakamoto (The University of Tokyo)
Harmonic measures in invariant random graphs on Gromov-hyperbolic spaces (日本語)
[ Abstract ]
In discrete group theory, a Cayley graph is a fundamental concept to view a finitely generated group as a geometric object itself. For example, the planar lattice is constructed from the free abelian group Z^2, and the 4-regular tree is constructed from the free group F_2. A group acts naturally on its Cayley graph as translations, so Bernoulli percolations on the graph can be viewed as a random graph whose distribution is invariant under the group action. In this talk, after reviewing previous works on such group-invariant random graphs, I will present my result concerning random walks on group-invariant random graphs over Gromov-hyperbolic groups. If time permits, I would also like to talk about the analogue in continuous spaces, such as Lie groups or symmetric spaces.
In discrete group theory, a Cayley graph is a fundamental concept to view a finitely generated group as a geometric object itself. For example, the planar lattice is constructed from the free abelian group Z^2, and the 4-regular tree is constructed from the free group F_2. A group acts naturally on its Cayley graph as translations, so Bernoulli percolations on the graph can be viewed as a random graph whose distribution is invariant under the group action. In this talk, after reviewing previous works on such group-invariant random graphs, I will present my result concerning random walks on group-invariant random graphs over Gromov-hyperbolic groups. If time permits, I would also like to talk about the analogue in continuous spaces, such as Lie groups or symmetric spaces.
2024/10/25
Colloquium
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.
Hokuto Konno (Graduate School of Mathematical Sciences, The University of Tokyo)
Diffeomorphism group and gauge theory (JAPANESE)
https://forms.gle/96tZtBr1GhdHi1tZ9
In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.
Hokuto Konno (Graduate School of Mathematical Sciences, The University of Tokyo)
Diffeomorphism group and gauge theory (JAPANESE)
[ Abstract ]
The dimension 4 is special in the classification theory of manifolds, as it exhibits phenomena that occur exclusively in this dimension. It is now well-known that gauge theory, which involves the study of partial differential equations derived from physics on 4-dimensional manifolds, is a powerful tool for discovering and exploring such phenomena. On the other hand, in the topology of manifolds, the diffeomorphism group, which is the automorphism group of a given smooth manifold, is a fundamental object of interest. Even for higher-dimensional manifolds, whose classification was largely settled more than half a century ago, significant progress continues to be made, and this remains a major trend in recent topology. Nevertheless, the systematic study of the diffeomorphism groups of 4-dimensional manifolds, particularly from the perspective of gauge theory, had long remained underexplored, with only a few pioneering results. However, in recent years, there has been rapid progress in the "gauge theory for families", which is the application of gauge theory to families of 4-dimensional manifolds, leading to new insights into the diffeomorphism groups of 4-manifolds. Specifically, it has turned out that, similar to the classification theory of manifolds, the diffeomorphism groups of 4-manifolds exhibit phenomena that are unique to this dimension. In this talk, I will provide an overview of these recent developments.
[ Reference URL ]The dimension 4 is special in the classification theory of manifolds, as it exhibits phenomena that occur exclusively in this dimension. It is now well-known that gauge theory, which involves the study of partial differential equations derived from physics on 4-dimensional manifolds, is a powerful tool for discovering and exploring such phenomena. On the other hand, in the topology of manifolds, the diffeomorphism group, which is the automorphism group of a given smooth manifold, is a fundamental object of interest. Even for higher-dimensional manifolds, whose classification was largely settled more than half a century ago, significant progress continues to be made, and this remains a major trend in recent topology. Nevertheless, the systematic study of the diffeomorphism groups of 4-dimensional manifolds, particularly from the perspective of gauge theory, had long remained underexplored, with only a few pioneering results. However, in recent years, there has been rapid progress in the "gauge theory for families", which is the application of gauge theory to families of 4-dimensional manifolds, leading to new insights into the diffeomorphism groups of 4-manifolds. Specifically, it has turned out that, similar to the classification theory of manifolds, the diffeomorphism groups of 4-manifolds exhibit phenomena that are unique to this dimension. In this talk, I will provide an overview of these recent developments.
https://forms.gle/96tZtBr1GhdHi1tZ9
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