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Seminar information archive
Seminar information archive ～04/30｜Today's seminar 05/01 | Future seminars 05/02～
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Tatsuki Kuwagaki ( Kyoto University)
On the generic existence of WKB spectral networks/Stokes graphs (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Tatsuki Kuwagaki ( Kyoto University)
On the generic existence of WKB spectral networks/Stokes graphs (JAPANESE)
[ Abstract ]
The foliation determined by a quadratic differential on a Riemann surface is a classical object of study. In particular, considering leaves through zero points has been of interest in connection with WKB analysis, Teichmüller theory, and quantum field theory. WKB spectral network (or Stokes graph) is a higher-order-differential version of this notion. In this talk, I will discuss the proof of existence of WKB spectral network for a large class of differentials. If time permits, I will explain its relationship with Lagrangian intersection Floer theory.
[ Reference URL ]The foliation determined by a quadratic differential on a Riemann surface is a classical object of study. In particular, considering leaves through zero points has been of interest in connection with WKB analysis, Teichmüller theory, and quantum field theory. WKB spectral network (or Stokes graph) is a higher-order-differential version of this notion. In this talk, I will discuss the proof of existence of WKB spectral network for a large class of differentials. If time permits, I will explain its relationship with Lagrangian intersection Floer theory.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/10/21
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Atsushi Hayashimoto (National Institute of Technology Nagano College)
. (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Atsushi Hayashimoto (National Institute of Technology Nagano College)
. (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.
Kohei Noda (Institute for Industrial Mathematics, Kyushu University)
Scaling limits of non-Hermitian Wishart random matrices and their applications (日本語)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Kohei Noda (Institute for Industrial Mathematics, Kyushu University)
Scaling limits of non-Hermitian Wishart random matrices and their applications (日本語)
[ Abstract ]
This talk is based on joint work and an ongoing project with Sung-Soo Byun (Seoul National University) on the scaling limits of non-Hermitian Wishart random matrices, which were introduced in the context of quantum chromodynamics with a baryon chemical potential, and their probabilistic applications. We present a robust argument, a generalized Christoffel-Darboux type identity, to obtain the scaling limits of eigenvalue point processes (determinantal/Pfaffian point processes) for non-Hermitian Wishart ensembles. Additionally, I will discuss the fluctuation of real eigenvalues in non-Hermitian real Wishart ensembles.
This talk is based on joint work and an ongoing project with Sung-Soo Byun (Seoul National University) on the scaling limits of non-Hermitian Wishart random matrices, which were introduced in the context of quantum chromodynamics with a baryon chemical potential, and their probabilistic applications. We present a robust argument, a generalized Christoffel-Darboux type identity, to obtain the scaling limits of eigenvalue point processes (determinantal/Pfaffian point processes) for non-Hermitian Wishart ensembles. Additionally, I will discuss the fluctuation of real eigenvalues in non-Hermitian real Wishart ensembles.
2024/10/18
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Jennifer Li (Princeton University)
Rational surfaces with a non-arithmetic automorphism group (英語)
Jennifer Li (Princeton University)
Rational surfaces with a non-arithmetic automorphism group (英語)
[ Abstract ]
In [Tot12], Totaro gave examples of a K3 surface such that its automorphism group is not commensurable with an arithmetic group, answering a question of Mazur. We give examples of rational surfaces with the same property. Our examples Y are log Calabi-Yau surfaces, i.e., there is a reduced normal crossing divisor D in Y such that KY+D=0. This is joint work with Sebastián Torres.
In [Tot12], Totaro gave examples of a K3 surface such that its automorphism group is not commensurable with an arithmetic group, answering a question of Mazur. We give examples of rational surfaces with the same property. Our examples Y are log Calabi-Yau surfaces, i.e., there is a reduced normal crossing divisor D in Y such that KY+D=0. This is joint work with Sebastián Torres.
2024/10/17
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.
Makoto Enokizono (The University of Tokyo)
Slope inequalities for fibered complex surfaces (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Makoto Enokizono (The University of Tokyo)
Slope inequalities for fibered complex surfaces (JAPANESE)
[ Abstract ]
Slope inequalities of fibered surfaces are important in relation to the classification of algebraic surfaces and the complex structure of Lefschetz fibrations in four-dimensional topology. It is also known that many slope inequalities for semi-stable fibered surfaces can be derived from the intersection theory on the moduli space of stable curves. In this talk, after outlining the background of these studies, I will explain how various slope inequalities can be obtained for fibered surfaces that are not necessarily semi-stable by extending the discussion of the moduli space.
[ Reference URL ]Slope inequalities of fibered surfaces are important in relation to the classification of algebraic surfaces and the complex structure of Lefschetz fibrations in four-dimensional topology. It is also known that many slope inequalities for semi-stable fibered surfaces can be derived from the intersection theory on the moduli space of stable curves. In this talk, after outlining the background of these studies, I will explain how various slope inequalities can be obtained for fibered surfaces that are not necessarily semi-stable by extending the discussion of the moduli space.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/10/16
Infinite Analysis Seminar Tokyo
15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Davide Dal Martello (Rikkyo University)
Convolutions, factorizations, and clusters from Painlevé VI (English)
Davide Dal Martello (Rikkyo University)
Convolutions, factorizations, and clusters from Painlevé VI (English)
[ Abstract ]
The Painlevé VI equation governs the isomonodromic deformation problem of both 2-dimensional Fuchsian and 3-dimensional Birkhoff systems. Through duality, this feature identifies the two systems. We prove this bijection admits a more transparent middle convolution formulation, which unlocks a monodromic translation involving the Killing factorization. Moreover, exploiting a higher Teichmüller parametrization of the monodromy group, Okamoto's birational map of PVI is given a new realization as a cluster transformation. Time permitting, we conclude with a taste of the quantum version of these constructions.
The Painlevé VI equation governs the isomonodromic deformation problem of both 2-dimensional Fuchsian and 3-dimensional Birkhoff systems. Through duality, this feature identifies the two systems. We prove this bijection admits a more transparent middle convolution formulation, which unlocks a monodromic translation involving the Killing factorization. Moreover, exploiting a higher Teichmüller parametrization of the monodromy group, Okamoto's birational map of PVI is given a new realization as a cluster transformation. Time permitting, we conclude with a taste of the quantum version of these constructions.
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Pierre Colmez (Sorbonne University)
On the factorisation of Beilinson-Kato system (English)
Pierre Colmez (Sorbonne University)
On the factorisation of Beilinson-Kato system (English)
[ Abstract ]
I will explain how one can factor Beilinson-Kato system as a product of two modular symbols, an algebraic incarnation of Rankin's method. This is joint work with Shanwen Wang.
I will explain how one can factor Beilinson-Kato system as a product of two modular symbols, an algebraic incarnation of Rankin's method. This is joint work with Shanwen Wang.
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Kengo Nakai (Okayama University)
Data-driven modeling from biased small training data (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Kengo Nakai (Okayama University)
Data-driven modeling from biased small training data (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2024/10/10
Tokyo Probability Seminar
10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)
The lecture is in the morning. The classroom is 122. This is a joint seminar with the Infinite Analysis Seminar Tokyo. No teatime today.
Chiara Franceschini (University of Modena and Reggio Emilia)
Harmonic models out of equilibrium: duality relations and invariant measure (英語)
The lecture is in the morning. The classroom is 122. This is a joint seminar with the Infinite Analysis Seminar Tokyo. No teatime today.
Chiara Franceschini (University of Modena and Reggio Emilia)
Harmonic models out of equilibrium: duality relations and invariant measure (英語)
[ Abstract ]
Zero-range interacting systems of Harmonic type have been recently introduced by Frassek, Giardinà and Kurchan [JSP 2020] from the integrable XXX Hamiltonian with non compact spins. In this talk I will introduce this one parameter family of models on a one dimensional lattice with open boundary whose dynamics describes redistribution of energy or jump of particles between nearest neighbor sites. These models belong to the same macroscopic class of the KMP model, introduced in 1982 by Kipnis Marchioro and Presutti. First, I will show their similar algebraic structure as well as their duality relations. Second, I will present how to explicitly characterize the invariant measure out of equilibrium, a task that is, in general, quite difficult in this context and it has been achieved in very few cases, e.g. the well known exclusion process. As an application, thanks to this characterization, it is possible to compute formulas predicted by macroscopic fluctuation theory. This is from joint works with: Gioia Carinci, Rouven Frassek, Davide Gabrielli, Cirstian Giarinà, Frank Redig and Dimitrios Tsagkarogiannis.
Zero-range interacting systems of Harmonic type have been recently introduced by Frassek, Giardinà and Kurchan [JSP 2020] from the integrable XXX Hamiltonian with non compact spins. In this talk I will introduce this one parameter family of models on a one dimensional lattice with open boundary whose dynamics describes redistribution of energy or jump of particles between nearest neighbor sites. These models belong to the same macroscopic class of the KMP model, introduced in 1982 by Kipnis Marchioro and Presutti. First, I will show their similar algebraic structure as well as their duality relations. Second, I will present how to explicitly characterize the invariant measure out of equilibrium, a task that is, in general, quite difficult in this context and it has been achieved in very few cases, e.g. the well known exclusion process. As an application, thanks to this characterization, it is possible to compute formulas predicted by macroscopic fluctuation theory. This is from joint works with: Gioia Carinci, Rouven Frassek, Davide Gabrielli, Cirstian Giarinà, Frank Redig and Dimitrios Tsagkarogiannis.
Infinite Analysis Seminar Tokyo
10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Chiara Franceschini (University of Modena and Reggio Emilia)
Harmonic models out of equilibrium: duality relations and invariant measure (ENGLISH)
Chiara Franceschini (University of Modena and Reggio Emilia)
Harmonic models out of equilibrium: duality relations and invariant measure (ENGLISH)
[ Abstract ]
Zero-range interacting systems of Harmonic type have been recently introduced by Frassek, Giardinà and Kurchan [JSP 2020] from the integrable XXX Hamiltonian with non compact spins. In this talk I will introduce this one parameter family of models on a one dimensional lattice with open boundary whose dynamics describes redistribution of energy or jump of particles between nearest neighbor sites. These models belong to the same macroscopic class of the KMP model, introduced in 1982 by Kipnis Marchioro and Presutti. First, I will show their similar algebraic structure as well as their duality relations. Second, I will present how to explicitly characterize the invariant measure out of equilibrium, a task that is, in general, quite difficult in this context and it has been achieved in very few cases, e.g. the well known exclusion process. As an application, thanks to this characterization, it is possible to compute formulas predicted by macroscopic fluctuation theory.
This is from joint works with: Gioia Carinci, Rouven Frassek, Davide Gabrielli, Cirstian Giarinà, Frank Redig and Dimitrios Tsagkarogiannis.
Zero-range interacting systems of Harmonic type have been recently introduced by Frassek, Giardinà and Kurchan [JSP 2020] from the integrable XXX Hamiltonian with non compact spins. In this talk I will introduce this one parameter family of models on a one dimensional lattice with open boundary whose dynamics describes redistribution of energy or jump of particles between nearest neighbor sites. These models belong to the same macroscopic class of the KMP model, introduced in 1982 by Kipnis Marchioro and Presutti. First, I will show their similar algebraic structure as well as their duality relations. Second, I will present how to explicitly characterize the invariant measure out of equilibrium, a task that is, in general, quite difficult in this context and it has been achieved in very few cases, e.g. the well known exclusion process. As an application, thanks to this characterization, it is possible to compute formulas predicted by macroscopic fluctuation theory.
This is from joint works with: Gioia Carinci, Rouven Frassek, Davide Gabrielli, Cirstian Giarinà, Frank Redig and Dimitrios Tsagkarogiannis.
2024/10/08
Operator Algebra Seminars
16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)
Fuyuta Komura (RIKEN)
Weyl groups of groupoid $C^*$-algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Fuyuta Komura (RIKEN)
Weyl groups of groupoid $C^*$-algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar of Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Erik Skibsted (Aarhus University)
Scattering subspace for time-periodic $N$-body Schrödinger operators (English)
https://forms.gle/it1Kc4voAXK5vpcB9
Erik Skibsted (Aarhus University)
Scattering subspace for time-periodic $N$-body Schrödinger operators (English)
[ Abstract ]
We propose a definition of a scattering subspace for many-body Schrödinger operators with time-periodic short-range pair-potentials. This in given in geometric terms. We then show that all channel wave operators exist, and that their ranges span the scattering subspace. This may possibly serve as an intermediate step for proving the longstanding open problem of asymptotic completeness, which may be reformulated as the assertion that the scattering subspace is the orthogonal subspace of the pure point subspace of the monodromy operator.
[ Reference URL ]We propose a definition of a scattering subspace for many-body Schrödinger operators with time-periodic short-range pair-potentials. This in given in geometric terms. We then show that all channel wave operators exist, and that their ranges span the scattering subspace. This may possibly serve as an intermediate step for proving the longstanding open problem of asymptotic completeness, which may be reformulated as the assertion that the scattering subspace is the orthogonal subspace of the pure point subspace of the monodromy operator.
https://forms.gle/it1Kc4voAXK5vpcB9
Tuesday Seminar on Topology
17:00-18:30 Room #ハイブリッド開催/123 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Hokuto Konno (The University of Tokyo)
Dehn twists on 4-manifolds (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Hokuto Konno (The University of Tokyo)
Dehn twists on 4-manifolds (JAPANESE)
[ Abstract ]
Dehn twists on surfaces form a basic class of diffeomorphisms. On 4-manifolds, an analogue of Dehn twist can be defined by considering twists along Seifert fibered 3-manifolds. In this talk, I will explain how this type of diffeomorphism exhibits interesting properties from the perspective of differential topology, and occasionally from the viewpoint of symplectic geometry as well. The proof involves gauge theory for families. This talk includes joint work with Abhishek Mallick and Masaki Taniguchi, as well as joint work with Jianfeng Lin, Anubhav Mukherjee, and Juan Muñoz-Echániz.
[ Reference URL ]Dehn twists on surfaces form a basic class of diffeomorphisms. On 4-manifolds, an analogue of Dehn twist can be defined by considering twists along Seifert fibered 3-manifolds. In this talk, I will explain how this type of diffeomorphism exhibits interesting properties from the perspective of differential topology, and occasionally from the viewpoint of symplectic geometry as well. The proof involves gauge theory for families. This talk includes joint work with Abhishek Mallick and Masaki Taniguchi, as well as joint work with Jianfeng Lin, Anubhav Mukherjee, and Juan Muñoz-Echániz.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/10/07
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shinichi Tajima (Niigata Univ.)
. (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Shinichi Tajima (Niigata Univ.)
. (Japanese)
[ Abstract ]
.
[ Reference URL ].
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/10/04
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Teppei Takamatsu (Kyoto University)
Arithmetic finiteness of Mukai varieties of genus 7 (日本語)
Teppei Takamatsu (Kyoto University)
Arithmetic finiteness of Mukai varieties of genus 7 (日本語)
[ Abstract ]
Fano threefolds over C with Picard number and index equal to 1 are known to be classified by their genus g (where 2≤g≤12 and g≠11). In particular, Mukai has shown that those with genus 7 can be described as hyperplane sections of a connected component of the 10-dimensional orthogonal Grassmannian.
In this talk, we discuss the arithmetic properties of these genus 7 threefolds and their higher-dimensional generalizations (called Mukai varieties of genus 7). More precisely, we consider the finiteness problem of varieties over a ring of S-integers (so called the Shafarevich conjecture), and the existence problem of varieties over the rational integer ring Z.
This talk is based on a joint work with Tetsushi Ito, Akihiro Kanemitsu, and Yuuji Tanaka.
Fano threefolds over C with Picard number and index equal to 1 are known to be classified by their genus g (where 2≤g≤12 and g≠11). In particular, Mukai has shown that those with genus 7 can be described as hyperplane sections of a connected component of the 10-dimensional orthogonal Grassmannian.
In this talk, we discuss the arithmetic properties of these genus 7 threefolds and their higher-dimensional generalizations (called Mukai varieties of genus 7). More precisely, we consider the finiteness problem of varieties over a ring of S-integers (so called the Shafarevich conjecture), and the existence problem of varieties over the rational integer ring Z.
This talk is based on a joint work with Tetsushi Ito, Akihiro Kanemitsu, and Yuuji Tanaka.
2024/10/03
Discrete mathematical modelling seminar
15:00-16:30 Room #270 (Graduate School of Math. Sci. Bldg.)
Anton Dzhamay (BIMSA, Beijing)
Some Examples of Geometric Deautonomization
Anton Dzhamay (BIMSA, Beijing)
Some Examples of Geometric Deautonomization
[ Abstract ]
It is well-known that many interesting examples of discrete Painlevé equations can be obtained from QRT mappings via a deautonomization process. There is an algebraic approach by B. Grammaticos, A. Ramani, and their collaborators, that uses the notion of singularity confinement to perform this process.
Recently, together with A. S. Carstea and T. Takenawa, we introduced the notion of geometric deautonomization of QRT maps based on a choice of a fiber in the QRT fibration. In this talk we present some examples of geometric deautonomization using a particular QRT map that appears in the discretization of the Nahm equations.
It is well-known that many interesting examples of discrete Painlevé equations can be obtained from QRT mappings via a deautonomization process. There is an algebraic approach by B. Grammaticos, A. Ramani, and their collaborators, that uses the notion of singularity confinement to perform this process.
Recently, together with A. S. Carstea and T. Takenawa, we introduced the notion of geometric deautonomization of QRT maps based on a choice of a fiber in the QRT fibration. In this talk we present some examples of geometric deautonomization using a particular QRT map that appears in the discretization of the Nahm equations.
2024/10/02
FJ-LMI Seminar
13:30-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Daniel CARO (Université de Caen Normandie)
Introduction to arithmetic D-modules (英語)
https://fj-lmi.cnrs.fr/seminars/
Daniel CARO (Université de Caen Normandie)
Introduction to arithmetic D-modules (英語)
[ Abstract ]
In this talk, I will give a brief overview of the theory of D-arithmetic modules, initiated by P. Berthelot in the 90's. By replacing the analytic or complex algebraic varieties by algebraic varieties defined over a field of characteristic p>0, this corresponds to an arithmetic analogue of the usual theory of D-modules. This makes it possible to obtain categories of p-adic objects associated with varieties of characteristic p; these p-adic coefficients satisfying a six functors formalism as expected. Via the de Rham cohomology associated with the constant arithmetic D-module, we obtain a p-adic interpretation and the rationality of the Weil zeta function, an arithmetic avatar of the Riemann zeta function, as well as a p-adic analogue of the Riemann hypothesis.
[ Reference URL ]In this talk, I will give a brief overview of the theory of D-arithmetic modules, initiated by P. Berthelot in the 90's. By replacing the analytic or complex algebraic varieties by algebraic varieties defined over a field of characteristic p>0, this corresponds to an arithmetic analogue of the usual theory of D-modules. This makes it possible to obtain categories of p-adic objects associated with varieties of characteristic p; these p-adic coefficients satisfying a six functors formalism as expected. Via the de Rham cohomology associated with the constant arithmetic D-module, we obtain a p-adic interpretation and the rationality of the Weil zeta function, an arithmetic avatar of the Riemann zeta function, as well as a p-adic analogue of the Riemann hypothesis.
https://fj-lmi.cnrs.fr/seminars/
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Hui Gao (Southern University of Science and Technology)
Filtered integral Sen theory (English)
Hui Gao (Southern University of Science and Technology)
Filtered integral Sen theory (English)
[ Abstract ]
Using the Breuil--Kisin module attached to an integral crystalline representation, one can define an integral Hodge filtration whose behavior is closely related to arithmetic and geometry of the representation. In this talk, we discuss vanishing and torsion bound on graded pieces of this filtration, using a filtered integral Sen theory as key tool. This is joint work with Tong Liu.
Using the Breuil--Kisin module attached to an integral crystalline representation, one can define an integral Hodge filtration whose behavior is closely related to arithmetic and geometry of the representation. In this talk, we discuss vanishing and torsion bound on graded pieces of this filtration, using a filtered integral Sen theory as key tool. This is joint work with Tong Liu.
2024/10/01
Tuesday Seminar of Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Patrícia Gonçalves (Instituto Superior Técnico)
Hydrodynamics, fluctuations, and universality of exclusion processes (English)
Patrícia Gonçalves (Instituto Superior Técnico)
Hydrodynamics, fluctuations, and universality of exclusion processes (English)
[ Abstract ]
In the seventies, Frank Spitzer introduced interacting particle systems to the mathematics community. These systems consist of particles evolving randomly according to Markovian dynamics that conserve certain quantities. Interacting particle systems were already known in the physics and biophysics communities and served as toy models for a variety of interesting phenomena. One of the most classical interacting particle systems is the exclusion process, where particles evolve in a discrete space according to a transition probability, but at each site, only one particle is allowed. One of the goals of studying these models is to derive their hydrodynamic limit, i.e., to deduce the macroscopic equations governing the space-time evolution of the conserved quantities of the system from the underlying random motion of the microscopic particles.
In this talk, I will review the derivation of these limits for the exclusion process. I will also discuss their equilibrium fluctuations, i.e., the fluctuations around the typical profile when the system starts from the invariant measure. Our focus will then shift to the two-species exclusion process, a system with two conservation laws, namely particles of type A and B. We will see that for proper linear combinations of the conserved quantities, their evolution is autonomous. This advances our understanding of the universal behavior of these systems. This presentation is based on joint work with G. Cannizzaro, R. Misturini, and A. Occelli.
In the seventies, Frank Spitzer introduced interacting particle systems to the mathematics community. These systems consist of particles evolving randomly according to Markovian dynamics that conserve certain quantities. Interacting particle systems were already known in the physics and biophysics communities and served as toy models for a variety of interesting phenomena. One of the most classical interacting particle systems is the exclusion process, where particles evolve in a discrete space according to a transition probability, but at each site, only one particle is allowed. One of the goals of studying these models is to derive their hydrodynamic limit, i.e., to deduce the macroscopic equations governing the space-time evolution of the conserved quantities of the system from the underlying random motion of the microscopic particles.
In this talk, I will review the derivation of these limits for the exclusion process. I will also discuss their equilibrium fluctuations, i.e., the fluctuations around the typical profile when the system starts from the invariant measure. Our focus will then shift to the two-species exclusion process, a system with two conservation laws, namely particles of type A and B. We will see that for proper linear combinations of the conserved quantities, their evolution is autonomous. This advances our understanding of the universal behavior of these systems. This presentation is based on joint work with G. Cannizzaro, R. Misturini, and A. Occelli.
Tokyo Probability Seminar
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
The classroom is 128. This is a joint seminar with the Tuesday Seminar of Analysis. No TeaTime today.
Patricia Goncalves (Instituto Superior Técnico)
Hydrodynamics, fluctuations, and universality of exclusion processes (英語)
The classroom is 128. This is a joint seminar with the Tuesday Seminar of Analysis. No TeaTime today.
Patricia Goncalves (Instituto Superior Técnico)
Hydrodynamics, fluctuations, and universality of exclusion processes (英語)
[ Abstract ]
In the seventies, Frank Spitzer introduced interacting particle systems to the mathematics community. These systems consist of particles evolving randomly according to Markovian dynamics that conserve certain quantities. Interacting particle systems were already known in the physics and biophysics communities and served as toy models for a variety of interesting phenomena. One of the most classical interacting particle systems is the exclusion process, where particles evolve in a discrete space according to a transition probability, but at each site, only one particle is allowed. One of the goals of studying these models is to derive their hydrodynamic limit, i.e., to deduce the macroscopic equations governing the space-time evolution of the conserved quantities of the system from the underlying random motion of the microscopic particles.
In this talk, I will review the derivation of these limits for the exclusion process. I will also discuss their equilibrium fluctuations, i.e., the fluctuations around the typical profile when the system starts from the invariant measure. Our focus will then shift to the two-species exclusion process, a system with two conservation laws, namely particles of type A and B. We will see that for proper linear combinations of the conserved quantities, their evolution is autonomous. This advances our understanding of the universal behavior of these systems. This presentation is based on joint work with G. Cannizzaro, R. Misturini, and A. Occelli.
In the seventies, Frank Spitzer introduced interacting particle systems to the mathematics community. These systems consist of particles evolving randomly according to Markovian dynamics that conserve certain quantities. Interacting particle systems were already known in the physics and biophysics communities and served as toy models for a variety of interesting phenomena. One of the most classical interacting particle systems is the exclusion process, where particles evolve in a discrete space according to a transition probability, but at each site, only one particle is allowed. One of the goals of studying these models is to derive their hydrodynamic limit, i.e., to deduce the macroscopic equations governing the space-time evolution of the conserved quantities of the system from the underlying random motion of the microscopic particles.
In this talk, I will review the derivation of these limits for the exclusion process. I will also discuss their equilibrium fluctuations, i.e., the fluctuations around the typical profile when the system starts from the invariant measure. Our focus will then shift to the two-species exclusion process, a system with two conservation laws, namely particles of type A and B. We will see that for proper linear combinations of the conserved quantities, their evolution is autonomous. This advances our understanding of the universal behavior of these systems. This presentation is based on joint work with G. Cannizzaro, R. Misturini, and A. Occelli.
2024/09/30
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.
Naotaka Kajino (Kyoto University)
Heat kernel estimates for boundary traces of reflected diffusions on uniform domains
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Naotaka Kajino (Kyoto University)
Heat kernel estimates for boundary traces of reflected diffusions on uniform domains
[ Abstract ]
This talk is aimed at presenting the results of the speaker's recent joint work (arXiv:2312.08546) with Mathav Murugan (University of British Columbia) on the boundary trace processes of reflected diffusions on uniform domains. We obtain stable-like heat kernel estimates for such a boundary trace process when the diffusion on the underlying ambient space satisfies sub-Gaussian heat kernel estimates. Our arguments rely on new results of independent interest such as sharp two-sided estimates and the volume doubling property of the harmonic measure, the existence of a continuous extension of the Na\"im kernel to the topological boundary, and the Doob--Na\"im formula identifying the Dirichlet form of the boundary trace process as the pure-jump Dirichlet form whose jump kernel with respect to the harmonic measure is exactly (the continuous extension of) the Na\"im kernel.
This talk is aimed at presenting the results of the speaker's recent joint work (arXiv:2312.08546) with Mathav Murugan (University of British Columbia) on the boundary trace processes of reflected diffusions on uniform domains. We obtain stable-like heat kernel estimates for such a boundary trace process when the diffusion on the underlying ambient space satisfies sub-Gaussian heat kernel estimates. Our arguments rely on new results of independent interest such as sharp two-sided estimates and the volume doubling property of the harmonic measure, the existence of a continuous extension of the Na\"im kernel to the topological boundary, and the Doob--Na\"im formula identifying the Dirichlet form of the boundary trace process as the pure-jump Dirichlet form whose jump kernel with respect to the harmonic measure is exactly (the continuous extension of) the Na\"im kernel.
2024/09/18
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Ishan Levy (University of Copenhagen)
Telescopic stable homotopy theory (English)
Ishan Levy (University of Copenhagen)
Telescopic stable homotopy theory (English)
[ Abstract ]
Chromatic homotopy theory attempts to study the stable homotopy category by breaking it into v_n-periodic layers corresponding to height n formal groups. There are two natural ways to do this, via either the K(n)-localizations which are computationally accessible, or via the T(n)-localizations, which detect the v_n-periodic parts of the stable homotopy groups of spheres. Ravenel's telescope conjecture asks that these two localizations agree. For n at least 2 and all primes, I will discuss counterexamples to Ravenel’s telescope conjecture. Our counterexamples come from using trace methods to compute the T(n) and K(n)-localizations of the algebraic K-theory of a family of ring spectra, which in the case n=2 are certain finite Galois extensions of the K(1)-local sphere. I will then explain that this can be used to obtain an infinite family of elements in the v_n-periodic stable homotopy groups of spheres, giving the best known lower bound on the asymptotic average ranks of the stable stems. Finally, I will explain that the Galois group of the T(n)-local category agrees with that of the K(n)-local category, and how the failure of the telescope conjecture comes entirely from the failure of Galois hyperdescent. This talk comes from projects that are joint with Burklund, Carmeli, Clausen, Hahn, Schlank, and Yanovski.
Chromatic homotopy theory attempts to study the stable homotopy category by breaking it into v_n-periodic layers corresponding to height n formal groups. There are two natural ways to do this, via either the K(n)-localizations which are computationally accessible, or via the T(n)-localizations, which detect the v_n-periodic parts of the stable homotopy groups of spheres. Ravenel's telescope conjecture asks that these two localizations agree. For n at least 2 and all primes, I will discuss counterexamples to Ravenel’s telescope conjecture. Our counterexamples come from using trace methods to compute the T(n) and K(n)-localizations of the algebraic K-theory of a family of ring spectra, which in the case n=2 are certain finite Galois extensions of the K(1)-local sphere. I will then explain that this can be used to obtain an infinite family of elements in the v_n-periodic stable homotopy groups of spheres, giving the best known lower bound on the asymptotic average ranks of the stable stems. Finally, I will explain that the Galois group of the T(n)-local category agrees with that of the K(n)-local category, and how the failure of the telescope conjecture comes entirely from the failure of Galois hyperdescent. This talk comes from projects that are joint with Burklund, Carmeli, Clausen, Hahn, Schlank, and Yanovski.
2024/09/11
FJ-LMI Seminar
13:30-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Çağrı SERT (Univeristy of Warwick)
Counting limit theorems for representations of Gromov-hyperbolic groups (英語)
https://fj-lmi.cnrs.fr/seminars/
Çağrı SERT (Univeristy of Warwick)
Counting limit theorems for representations of Gromov-hyperbolic groups (英語)
[ Abstract ]
Let Г be a Gromov-hyperbolic group and S a finite symmetric generating set. The choice of S determines a metric on Г (namely the graph metric on the associated Cayley graph).
Given a representation ρ: Г→GL_d(R), we are interested in obtaining probabilistic limit theorems for the deterministic sequence of spherical averages (with respect to S-metric) for various numerical quantities (such as the operator norm) associated to elements of Г via the representation. We will discuss a general law of large numbers and more refined limit theorems such as central limit theorem and large deviations. Time permitting, connections with the results of Lubotzky–Mozes–Raghunathan and Kaimanovich–Kapovich–Schupp will also be mentioned. Joint work with Stephen Cantrell.
[ Reference URL ]Let Г be a Gromov-hyperbolic group and S a finite symmetric generating set. The choice of S determines a metric on Г (namely the graph metric on the associated Cayley graph).
Given a representation ρ: Г→GL_d(R), we are interested in obtaining probabilistic limit theorems for the deterministic sequence of spherical averages (with respect to S-metric) for various numerical quantities (such as the operator norm) associated to elements of Г via the representation. We will discuss a general law of large numbers and more refined limit theorems such as central limit theorem and large deviations. Time permitting, connections with the results of Lubotzky–Mozes–Raghunathan and Kaimanovich–Kapovich–Schupp will also be mentioned. Joint work with Stephen Cantrell.
https://fj-lmi.cnrs.fr/seminars/
Lie Groups and Representation Theory
13:30-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Joint with FJ-LMI seminar.
Çağrı SERT (Univeristy of Warwick)
Counting limit theorems for representations of Gromov-hyperbolic groups (English)
Joint with FJ-LMI seminar.
Çağrı SERT (Univeristy of Warwick)
Counting limit theorems for representations of Gromov-hyperbolic groups (English)
[ Abstract ]
Let Г be a Gromov-hyperbolic group and S a finite symmetric generating set. The choice of S determines a metric on Г (namely the graph metric on the associated Cayley graph).
Given a representation ρ: Г→GL_d(R), we are interested in obtaining probabilistic limit theorems for the deterministic sequence of spherical averages (with respect to S-metric) for various numerical quantities (such as the operator norm) associated to elements of Г via the representation. We will discuss a general law of large numbers and more refined limit theorems such as central limit theorem and large deviations. Time permitting, connections with the results of Lubotzky–Mozes–Raghunathan and Kaimanovich–Kapovich–Schupp will also be mentioned. Joint work with Stephen Cantrell.
Let Г be a Gromov-hyperbolic group and S a finite symmetric generating set. The choice of S determines a metric on Г (namely the graph metric on the associated Cayley graph).
Given a representation ρ: Г→GL_d(R), we are interested in obtaining probabilistic limit theorems for the deterministic sequence of spherical averages (with respect to S-metric) for various numerical quantities (such as the operator norm) associated to elements of Г via the representation. We will discuss a general law of large numbers and more refined limit theorems such as central limit theorem and large deviations. Time permitting, connections with the results of Lubotzky–Mozes–Raghunathan and Kaimanovich–Kapovich–Schupp will also be mentioned. Joint work with Stephen Cantrell.
2024/08/19
thesis presentations
14:00-15:15 Room #128 (Graduate School of Math. Sci. Bldg.)
OHARA Kazuma ( )
Hecke algebra isomorphisms for tame types
（馴分岐なタイプに付随するHecke環の同型について）
OHARA Kazuma ( )
Hecke algebra isomorphisms for tame types
（馴分岐なタイプに付随するHecke環の同型について）
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