## Seminar information archive

Seminar information archive ～02/01｜Today's seminar 02/02 | Future seminars 02/03～

#### Number Theory Seminar

17:00-18:00 Hybrid

A K-theoretic approach to geometric representation theory (ENGLISH)

**Jens Eberhardt**(University of Wuppertal)A K-theoretic approach to geometric representation theory (ENGLISH)

[ Abstract ]

Perverse sheaves and intersection cohomology are central objects in geometric representation theory. This talk is about their long-lost K-theoretic cousins, called K-motives. We will discuss definitions and basic properties of K-motives and explore potential applications to geometric representation theory. For example, K-motives shed a new light on Beilinson--Ginzburg--Soergel's Koszul duality -- a remarkable symmetry in the representation theory and geometry of two Langlands dual reductive groups. We will see that this new form of Koszul duality does not involve any gradings or mixed geometry which are as essential as mysterious in the classical approaches.

Perverse sheaves and intersection cohomology are central objects in geometric representation theory. This talk is about their long-lost K-theoretic cousins, called K-motives. We will discuss definitions and basic properties of K-motives and explore potential applications to geometric representation theory. For example, K-motives shed a new light on Beilinson--Ginzburg--Soergel's Koszul duality -- a remarkable symmetry in the representation theory and geometry of two Langlands dual reductive groups. We will see that this new form of Koszul duality does not involve any gradings or mixed geometry which are as essential as mysterious in the classical approaches.

### 2022/09/27

#### Classical Analysis

11:30-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Difference module and Homology 2 (JAPANESE)

Difference module and Homology 3 (JAPANESE)

**Koki Ito**(Osaka Electro-Communication University) 11:30-12:00Difference module and Homology 2 (JAPANESE)

**Koki Ito**(Osaka Electro-Communication University) 14:00-17:00Difference module and Homology 3 (JAPANESE)

### 2022/09/26

#### Classical Analysis

14:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Difference module and Homology 1 (JAPANESE)

**Koki Ito**(Osaka Electro-Communication University)Difference module and Homology 1 (JAPANESE)

### 2022/09/20

#### Operator Algebra Seminars

16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Honeycombs, polytopes, and representation theory (English)

[ Reference URL ]

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

**Robert Coquereaux**(CNRS/CPT)Honeycombs, polytopes, and representation theory (English)

[ Reference URL ]

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

### 2022/09/16

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

Prospects

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81167784080?pwd=VE94RnNYcmJZUXJ4QTIvZUhEQmVJZz09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State Univ.)Prospects

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81167784080?pwd=VE94RnNYcmJZUXJ4QTIvZUhEQmVJZz09

### 2022/09/15

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

Inverse problems for fluid dynamics

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81167784080?pwd=VE94RnNYcmJZUXJ4QTIvZUhEQmVJZz09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State Univ.)Inverse problems for fluid dynamics

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81167784080?pwd=VE94RnNYcmJZUXJ4QTIvZUhEQmVJZz09

### 2022/09/09

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

Inverse parabolic problems: recent results

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State Univ.)Inverse parabolic problems: recent results

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

### 2022/09/08

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

Inverse parabolic problems: recent results

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State Univ.)Inverse parabolic problems: recent results

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

### 2022/09/02

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

DN map for hyperbolic inverse problems

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State Univ.)DN map for hyperbolic inverse problems

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

### 2022/09/01

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

DN map for hyperbolic inverse problems

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State Univ.)DN map for hyperbolic inverse problems

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

### 2022/08/26

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

Recent researches on inverse problems by Carleman estimatesPart II + discussions on new aspects of mathematical analysis for inverse problems

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81424491417?pwd=T1BOMWtmZkhtY0pjUEs1NFZUZEYzQT09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State University)Recent researches on inverse problems by Carleman estimatesPart II + discussions on new aspects of mathematical analysis for inverse problems

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81424491417?pwd=T1BOMWtmZkhtY0pjUEs1NFZUZEYzQT09

### 2022/08/25

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

Recent researches on inverse problems by Carleman estimates Part I

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81424491417?pwd=T1BOMWtmZkhtY0pjUEs1NFZUZEYzQT09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State University )Recent researches on inverse problems by Carleman estimates Part I

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81424491417?pwd=T1BOMWtmZkhtY0pjUEs1NFZUZEYzQT09

### 2022/08/23

#### Tuesday Seminar of Analysis

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Quantitative homogenization for monotone, uniformly elliptic systems with random coefficients (English)

https://forms.gle/V1wxbYhT4mkPF4gY9

**Stefan Neukamm**(Dresden University/RIMS)Quantitative homogenization for monotone, uniformly elliptic systems with random coefficients (English)

[ Abstract ]

Motivated by homogenization of nonlinearly elastic composite materials, we study homogenization rates for elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. Under the assumption of a fast decay of correlations on scales larger than the microscale $\varepsilon$, we establish estimates of optimal order for the approximation of the homogenized operator by the method of representative volumes. Moreover, we discuss applications to nonlinear elasticity random laminates.

[ Reference URL ]Motivated by homogenization of nonlinearly elastic composite materials, we study homogenization rates for elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. Under the assumption of a fast decay of correlations on scales larger than the microscale $\varepsilon$, we establish estimates of optimal order for the approximation of the homogenized operator by the method of representative volumes. Moreover, we discuss applications to nonlinear elasticity random laminates.

https://forms.gle/V1wxbYhT4mkPF4gY9

### 2022/08/18

#### Discrete mathematical modelling seminar

15:00-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Different Hamiltonians for Painlevé Equations and their identification using geometry of the space of

initial conditions (English)

**Anton Dzhamay**(University of Northern Colorado)Different Hamiltonians for Painlevé Equations and their identification using geometry of the space of

initial conditions (English)

[ Abstract ]

It is well-known that differential Painlevé equations can be written in a Hamiltonian form. However, a coordinate form of such representation is far from unique – there are many very different Hamiltonians that result in the same differential Painlevé equation. In this paper we describe a systematic procedure of finding

changes of coordinates transforming different Hamiltonian systems into some canonical form.

Our approach is based on the Okamoto-Sakai geometric approach to Painlevé equations. We explain this approach using the differential P-IV equation as an example, but the procedure is general and can be easily adapted to other Painlevé equations as well. (Joint work with Galina Filipuk, Adam Ligeza and Alexander Stokes.)

It is well-known that differential Painlevé equations can be written in a Hamiltonian form. However, a coordinate form of such representation is far from unique – there are many very different Hamiltonians that result in the same differential Painlevé equation. In this paper we describe a systematic procedure of finding

changes of coordinates transforming different Hamiltonian systems into some canonical form.

Our approach is based on the Okamoto-Sakai geometric approach to Painlevé equations. We explain this approach using the differential P-IV equation as an example, but the procedure is general and can be easily adapted to other Painlevé equations as well. (Joint work with Galina Filipuk, Adam Ligeza and Alexander Stokes.)

### 2022/08/17

#### thesis presentations

13:00-14:15 Online

A study on cohomological Donaldson-Thomas invariants

[ Reference URL ]

https://forms.gle/cGq4sCUFSLjJqPw97

**KINJO Tasuki**(Graduate School of Mathematical Sciences University of Tokyo)A study on cohomological Donaldson-Thomas invariants

[ Reference URL ]

https://forms.gle/cGq4sCUFSLjJqPw97

### 2022/07/26

#### Tuesday Seminar of Analysis

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Periodic homogenization of non-symmetric jump-type processes with drifts (Japanese)

https://forms.gle/ewZEy1jAXrAhWx1Q8

**KUMAGAI Takashi**(Waseda University)Periodic homogenization of non-symmetric jump-type processes with drifts (Japanese)

[ Abstract ]

Homogenization problem is one of the classical problems in analysis and probability which is very actively studied recently. In this talk, we consider homogenization problem for non-symmetric Lévy-type processes with drifts in periodic media. Under a proper scaling, we show the scaled processes converge weakly to Lévy processes on ${\mathds R}^d$. In particular, we completely characterize the limiting processes when the coefficient function of the drift part is bounded continuous, and the decay rate of the jumping measure is comparable to $r^{-1-\alpha}$ for $r>1$ in the spherical coordinate with $\alpha \in (0,\infty)$. Different scaling limits appear depending on the values of $\alpha$.

This talk is based on joint work with Xin Chen, Zhen-Qing Chen and Jian Wang (Ann. Probab. 2021).

[ Reference URL ]Homogenization problem is one of the classical problems in analysis and probability which is very actively studied recently. In this talk, we consider homogenization problem for non-symmetric Lévy-type processes with drifts in periodic media. Under a proper scaling, we show the scaled processes converge weakly to Lévy processes on ${\mathds R}^d$. In particular, we completely characterize the limiting processes when the coefficient function of the drift part is bounded continuous, and the decay rate of the jumping measure is comparable to $r^{-1-\alpha}$ for $r>1$ in the spherical coordinate with $\alpha \in (0,\infty)$. Different scaling limits appear depending on the values of $\alpha$.

This talk is based on joint work with Xin Chen, Zhen-Qing Chen and Jian Wang (Ann. Probab. 2021).

https://forms.gle/ewZEy1jAXrAhWx1Q8

### 2022/07/22

#### Colloquium

15:30-16:30 Hybrid

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].

Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZYtf-iorDIiGNXBzovQXlHZjH4iXVS6QB4t

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].

**Ryo Takada**(Graduate School of Mathematical Sciences, the University of Tokyo)Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)

[ Abstract ]

In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.

[ Reference URL ]In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZYtf-iorDIiGNXBzovQXlHZjH4iXVS6QB4t

### 2022/07/21

#### Seminar on Probability and Statistics

13:30-14:40 Room #- (Graduate School of Math. Sci. Bldg.)

[ Reference URL ]

https://forms.gle/JrtVRcQNgn9pug3F7

**( )**[ Reference URL ]

https://forms.gle/JrtVRcQNgn9pug3F7

### 2022/07/20

#### Number Theory Seminar

15:30-18:00 Hybrid

Completed prismatic F-crystals and crystalline local systems (ENGLISH)

Twisted differential operators in several variables (ENGLISH)

**Koji Shimizu**(UC Berkeley) 15:30-16:30Completed prismatic F-crystals and crystalline local systems (ENGLISH)

[ Abstract ]

Bhatt and Scholze introduced the absolute prismatic site of a p-adic ring and proved the equivalence of categories between prismatic F-crystals and lattices in crystalline representations in the CDVR case with perfect residue field. We will define a wider category of completed prismatic F-crystals in the relative case and explain its relation to the category of crystalline local systems. This is joint work with Heng Du, Tong Liu, and Yong Suk Moon.

Bhatt and Scholze introduced the absolute prismatic site of a p-adic ring and proved the equivalence of categories between prismatic F-crystals and lattices in crystalline representations in the CDVR case with perfect residue field. We will define a wider category of completed prismatic F-crystals in the relative case and explain its relation to the category of crystalline local systems. This is joint work with Heng Du, Tong Liu, and Yong Suk Moon.

**Pierre Houedry**(Université de Caen) 17:00-18:00Twisted differential operators in several variables (ENGLISH)

[ Abstract ]

The aim of my presentation is to give an overview of the results I obtained during the first year of my PhD. The theory of $q$-differences equations appeared a long time ago with the Birkhoff's work. It is well understood in the complex setting. In 2004, Lucia Di Vizio and Yves André, in the paper $q$-differences and p-adic local monodromy, gave an equivalence between certain type of $q$-differences equations and a certain type of classical differential equations in the p-adic setting. Recently, Adolfo Quiros, Bernard Le Stum and Michel Gros have been working on a generalization of this result not looking only for $q$-differences equations but also twisted equations in general. The framework that they develop is working for equations in one variable. The goal of my thesis is to generalize those results in several variables.

The aim of my presentation is to give an overview of the results I obtained during the first year of my PhD. The theory of $q$-differences equations appeared a long time ago with the Birkhoff's work. It is well understood in the complex setting. In 2004, Lucia Di Vizio and Yves André, in the paper $q$-differences and p-adic local monodromy, gave an equivalence between certain type of $q$-differences equations and a certain type of classical differential equations in the p-adic setting. Recently, Adolfo Quiros, Bernard Le Stum and Michel Gros have been working on a generalization of this result not looking only for $q$-differences equations but also twisted equations in general. The framework that they develop is working for equations in one variable. The goal of my thesis is to generalize those results in several variables.

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

Please see the reference URL for details on the online seminar.

Grothendieck enriched categories (Japanese)

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

Please see the reference URL for details on the online seminar.

**Yuki Imamura**(Osaka University)Grothendieck enriched categories (Japanese)

[ Abstract ]

Grothendieck圏は、入射的余生成子の存在や随伴関手定理の成立など、アーベル圏の中でも特に良い性質を持つことで知られる。通常Grothendieck圏は、生成子を持つ余完備なアーベル圏であって、フィルター余極限を取る関手が完全関手になるような圏として内在的な性質で以て定義されるが、加群圏の"良い部分圏"として実現できるという外在的な特徴づけ(Gabriel-Popescuの定理)も存在する。アーベル圏が自然なプレ加法圏(アーベル群の圏Ab上の豊穣圏)の構造を持つことから、Gabriel-Popescuの定理はAb-豊穣圏に対する定理だと思うことができる。本講演では、より一般のGrothendieckモノイダル圏V上の豊穣圏に対してGabriel-Popescuの定理の一般化を定式化し証明する。特にVとしてアーベル群の複体の圏Chを取ることによりGrothendieck圏のdg圏類似とそのGabriel-Popescuの定理が得られることも確認する。

[ Reference URL ]Grothendieck圏は、入射的余生成子の存在や随伴関手定理の成立など、アーベル圏の中でも特に良い性質を持つことで知られる。通常Grothendieck圏は、生成子を持つ余完備なアーベル圏であって、フィルター余極限を取る関手が完全関手になるような圏として内在的な性質で以て定義されるが、加群圏の"良い部分圏"として実現できるという外在的な特徴づけ(Gabriel-Popescuの定理)も存在する。アーベル圏が自然なプレ加法圏(アーベル群の圏Ab上の豊穣圏)の構造を持つことから、Gabriel-Popescuの定理はAb-豊穣圏に対する定理だと思うことができる。本講演では、より一般のGrothendieckモノイダル圏V上の豊穣圏に対してGabriel-Popescuの定理の一般化を定式化し証明する。特にVとしてアーベル群の複体の圏Chを取ることによりGrothendieck圏のdg圏類似とそのGabriel-Popescuの定理が得られることも確認する。

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

### 2022/07/12

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Cable knots and involutive Heegaard Floer homology (ENGLISH)

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

Pre-registration required. See our seminar webpage.

**Sungkyung Kang**(Center for Geometry and Physics, Institute of Basic Science)Cable knots and involutive Heegaard Floer homology (ENGLISH)

[ Abstract ]

Heegaard Floer homology (and its variants) carries an intrinsic symmetry, which conjecturally corresponds to the Pin(2)-equivariance in Seiberg-Witten Floer homology. By exploiting the symmetry, we prove that (odd,1)-cables of the figure-eight knots are linearly independent in the concordance group of rationally slice knots, and present a first example of rationally slice knots of complexity 1 which are not slice. Furthermore, we establish an explicit connection between involutive knot Floer theory and involutive bordered Floer theory of knot complements, and use it to prove a similar result for iterated cables of figure-eight knots. A part of this talk is based on a joint work with J. Hom, M. Stoffregen, and J. Park.

[ Reference URL ]Heegaard Floer homology (and its variants) carries an intrinsic symmetry, which conjecturally corresponds to the Pin(2)-equivariance in Seiberg-Witten Floer homology. By exploiting the symmetry, we prove that (odd,1)-cables of the figure-eight knots are linearly independent in the concordance group of rationally slice knots, and present a first example of rationally slice knots of complexity 1 which are not slice. Furthermore, we establish an explicit connection between involutive knot Floer theory and involutive bordered Floer theory of knot complements, and use it to prove a similar result for iterated cables of figure-eight knots. A part of this talk is based on a joint work with J. Hom, M. Stoffregen, and J. Park.

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### Operator Algebra Seminars

16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Relative Drinfeld centers associated to monoidal functors

[ Reference URL ]

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

**Mao Hoshino**(Univ. Tokyo)Relative Drinfeld centers associated to monoidal functors

[ Reference URL ]

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

### 2022/07/11

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

The CR Killing operator and Bernstein-Gelfand-Gelfand construction in CR geometry (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Yoshihiko Matsumoto**(Osaka University)The CR Killing operator and Bernstein-Gelfand-Gelfand construction in CR geometry (Japanese)

[ Abstract ]

In this talk, I introduce the CR Killing operator associated with compatible almost CR structures on contact manifolds, which describes trivial infinitesimal deformations generated by contact Hamiltonian vector fields, and discuss how it can also be reconstructed by the Bernstein-Gelfand-Gelfand construction in the general theory of parabolic geometries. The “modified” adjoint tractor connection defined by Cap (2008) plays a crucial role. If time permits, I’d also like to discuss what this observation might mean in relation to asymptotically complex hyperbolic Einstein metrics, which are bulk geometric structures for compatible almost CR structures at infinity.

[ Reference URL ]In this talk, I introduce the CR Killing operator associated with compatible almost CR structures on contact manifolds, which describes trivial infinitesimal deformations generated by contact Hamiltonian vector fields, and discuss how it can also be reconstructed by the Bernstein-Gelfand-Gelfand construction in the general theory of parabolic geometries. The “modified” adjoint tractor connection defined by Cap (2008) plays a crucial role. If time permits, I’d also like to discuss what this observation might mean in relation to asymptotically complex hyperbolic Einstein metrics, which are bulk geometric structures for compatible almost CR structures at infinity.

https://forms.gle/hYT2hVhDE3q1wDSh6

### 2022/07/07

#### Information Mathematics Seminar

16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)

Design and control of quantum computers XIII (Japanese)

**Yasunari Suzuki**(NTT)Design and control of quantum computers XIII (Japanese)

[ Abstract ]

How to use quantum computer II

How to use quantum computer II

### 2022/07/06

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

Please see the reference URL for details on the online seminar.

Cyclic polytopes and higher Auslander--Reiten theory 3 (English)

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

Please see the reference URL for details on the online seminar.

**Nicholas Williams**(The University of Tokyo)Cyclic polytopes and higher Auslander--Reiten theory 3 (English)

[ Abstract ]

This continues part 2. In the third talk, we consider the relationship between the objects from the first two talks. We explain how triangulations of even-dimensional cyclic polytopes may be interpreted in terms of tilting modules, cluster-tilting objects, or d-silting complexes. We then proceed in the d-silting framework, and show how the higher Stasheff--Tamari orders may be interpreted algebraically for even dimensions. We explain how this allows one to interpret odd-dimensional triangulations algebraically, namely, as equivalence classes of d-maximal green sequences. We briefly digress to consider the issue of equivalence of maximal green sequences itself. We then show how one can interpret the higher Stasheff--Tamari orders on equivalence classes of d-maximal green sequences. We finish by drawing out some consequences of this algebraic interpretation of the higher Stasheff--Tamari orders.

[ Reference URL ]This continues part 2. In the third talk, we consider the relationship between the objects from the first two talks. We explain how triangulations of even-dimensional cyclic polytopes may be interpreted in terms of tilting modules, cluster-tilting objects, or d-silting complexes. We then proceed in the d-silting framework, and show how the higher Stasheff--Tamari orders may be interpreted algebraically for even dimensions. We explain how this allows one to interpret odd-dimensional triangulations algebraically, namely, as equivalence classes of d-maximal green sequences. We briefly digress to consider the issue of equivalence of maximal green sequences itself. We then show how one can interpret the higher Stasheff--Tamari orders on equivalence classes of d-maximal green sequences. We finish by drawing out some consequences of this algebraic interpretation of the higher Stasheff--Tamari orders.

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

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