## Seminar information archive

Seminar information archive ～11/05｜Today's seminar 11/06 | Future seminars 11/07～

### 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.

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.)

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.)

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.)

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.)

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.)

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.

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.)

. (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.

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.

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

### 2024/10/23

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

一般化マルコフ数とそのSL(2,Z)行列化 (Japanese)

[ Reference URL ]

https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

**Yasuaki Gyoda**(The University of Tokyo)一般化マルコフ数とそのSL(2,Z)行列化 (Japanese)

[ Reference URL ]

https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

### 2024/10/22

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Diagonals of $C^*$-algebras

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Kei Ito**(Univ. Tokyo)Diagonals of $C^*$-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.

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.)

. (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.

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.)

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.

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.)

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.)

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.)

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.

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.)

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.)

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.)

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.

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

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190 Next >