## Seminar information archive

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

### 2019/07/24

#### thesis presentations

13:15-14:30 Room #128 (Graduate School of Math. Sci. Bldg.)

**OKADA Mao**### 2019/07/23

#### PDE Real Analysis Seminar

13:00-14:00 Room #056 (Graduate School of Math. Sci. Bldg.)

On the isoperimetric ratio over scalar-flat conformal classes (English)

**Tianling Jin**(The Hong Kong University of Science and Technology)On the isoperimetric ratio over scalar-flat conformal classes (English)

[ Abstract ]

Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $n$ with smooth boundary. Suppose that $(M,g)$ admits a scalar-flat conformal metric. We prove that the supremum of the isoperimetric ratio over the scalar-flat conformal class is strictly larger than the best constant of the isoperimetric inequality on Euclidean space, and consequently is achieved, if either (i) $n \geq 12$ and the boundary has a nonumbilic point; or (ii) $n \geq 10$, the boundary is umbilic and the Weyl tensor does not vanish at some boundary point. A crucial ingredient in the proof is the expansion of solutions to the conformal Laplacian equation with blowing up Dirichlet boundary conditions.

Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $n$ with smooth boundary. Suppose that $(M,g)$ admits a scalar-flat conformal metric. We prove that the supremum of the isoperimetric ratio over the scalar-flat conformal class is strictly larger than the best constant of the isoperimetric inequality on Euclidean space, and consequently is achieved, if either (i) $n \geq 12$ and the boundary has a nonumbilic point; or (ii) $n \geq 10$, the boundary is umbilic and the Weyl tensor does not vanish at some boundary point. A crucial ingredient in the proof is the expansion of solutions to the conformal Laplacian equation with blowing up Dirichlet boundary conditions.

### 2019/07/16

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Seifert vs. slice genera of knots in twist families and a characterization of braid axes (JAPANESE)

**Kimihiko Motegi**(Nihon University)Seifert vs. slice genera of knots in twist families and a characterization of braid axes (JAPANESE)

[ Abstract ]

Twisting a knot $K$ in $S^3$ along a disjoint unknot $c$ produces a twist family of knots $\{K_n\}$ indexed by the integers. Comparing the behaviors of the Seifert genus $g(K_n)$ and the slice genus $g_4(K_n)$ under twistings, we prove that if $g(K_n) - g_4(K_n) < C$ for some constant $C$ for infinitely many integers $n > 0$ or $g(K_n) / g_4(K_n)$ limits to $1$, then the winding number of $K$ about $c$ equals either zero or the wrapping number. As a key application, if $\{K_n\}$ or the mirror twist family $\{\overline{K_n}\}$ contains infinitely many tight fibered knots, then the latter must occur. This leads to the characterization that $c$ is a braid axis of $K$ if and only if both $\{K_n\}$ and $\{\overline{K_n}\}$ each contain infinitely many tight fibered knots. We also give a necessary and sufficient condition for $\{K_n\}$ to contain infinitely many L-space knots, and apply the characterization to prove that satellite L-space knots have braided patterns, which answers a question of both Baker-Moore and Hom in the positive. This result also implies an absence of essential Conway spheres for satellite L-space knots, which gives a partial answer to a conjecture of Lidman-Moore.

Twisting a knot $K$ in $S^3$ along a disjoint unknot $c$ produces a twist family of knots $\{K_n\}$ indexed by the integers. Comparing the behaviors of the Seifert genus $g(K_n)$ and the slice genus $g_4(K_n)$ under twistings, we prove that if $g(K_n) - g_4(K_n) < C$ for some constant $C$ for infinitely many integers $n > 0$ or $g(K_n) / g_4(K_n)$ limits to $1$, then the winding number of $K$ about $c$ equals either zero or the wrapping number. As a key application, if $\{K_n\}$ or the mirror twist family $\{\overline{K_n}\}$ contains infinitely many tight fibered knots, then the latter must occur. This leads to the characterization that $c$ is a braid axis of $K$ if and only if both $\{K_n\}$ and $\{\overline{K_n}\}$ each contain infinitely many tight fibered knots. We also give a necessary and sufficient condition for $\{K_n\}$ to contain infinitely many L-space knots, and apply the characterization to prove that satellite L-space knots have braided patterns, which answers a question of both Baker-Moore and Hom in the positive. This result also implies an absence of essential Conway spheres for satellite L-space knots, which gives a partial answer to a conjecture of Lidman-Moore.

### 2019/07/11

#### Information Mathematics Seminar

16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)

Functional Encryption from Bilinear Pairings (Japanese)

**Katsuyuki Takashima**(Mitsubishi Electric Co./Kyushu Univ.)Functional Encryption from Bilinear Pairings (Japanese)

[ Abstract ]

Explanation of functional encryption schemes from bilinear pairings

Explanation of functional encryption schemes from bilinear pairings

#### Mathematical Biology Seminar

15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Understanding The Seasonality of Dengue Disease Incidences From Empirical Data (ENGLISH)

**Dipo Aldila**(Universitas Indonesia)Understanding The Seasonality of Dengue Disease Incidences From Empirical Data (ENGLISH)

[ Abstract ]

Investigating the seasonality of dengue incidences is very important in dengue surveillance in regions with periodical climatic patterns. In lieu of the paradigm about dengue incidences varying seasonally in line with meteorology, this talk seeks to determine how well standard epidemic mo-dels (SIRUV) can capture such seasonality for better forecasts and optimal futuristic interventions. Once incidence data are assimilated by a periodic model, asymptotic analysis in relation to the long-term behavior of the dengue occurrences will be performed. For a test case, we employed an SIRUV model (later become IR model with QSSA method) to assimilate weekly dengue incidence data from the city of Jakarta, Indonesia, which we present in their raw and moving-average-filtered versions. To estimate a periodic parameter toward performing the asymptotic analysis, some optimization schemes were assigned returning magnitudes of the parameter that vary insignificantly across schemes. Furthermore, the computation results combined with the analytical results indicate that if the disease surveillance in the city does not improve, then the incidence will raise to a certain positive orbit and remain cyclical.

Investigating the seasonality of dengue incidences is very important in dengue surveillance in regions with periodical climatic patterns. In lieu of the paradigm about dengue incidences varying seasonally in line with meteorology, this talk seeks to determine how well standard epidemic mo-dels (SIRUV) can capture such seasonality for better forecasts and optimal futuristic interventions. Once incidence data are assimilated by a periodic model, asymptotic analysis in relation to the long-term behavior of the dengue occurrences will be performed. For a test case, we employed an SIRUV model (later become IR model with QSSA method) to assimilate weekly dengue incidence data from the city of Jakarta, Indonesia, which we present in their raw and moving-average-filtered versions. To estimate a periodic parameter toward performing the asymptotic analysis, some optimization schemes were assigned returning magnitudes of the parameter that vary insignificantly across schemes. Furthermore, the computation results combined with the analytical results indicate that if the disease surveillance in the city does not improve, then the incidence will raise to a certain positive orbit and remain cyclical.

### 2019/07/10

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Convergence theorems on multi-dimensional homogeneous quantum walks

**Hiroki Sako**(Niigata University)Convergence theorems on multi-dimensional homogeneous quantum walks

### 2019/07/09

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Mod 2 cohomology of moduli stacks of real vector bundles (ENGLISH)

**Florent Schaffhauser**(Université de Strasbourg)Mod 2 cohomology of moduli stacks of real vector bundles (ENGLISH)

[ Abstract ]

The rational cohomology ring of the moduli stack of holomorphic vector bundles of fixed rank and degree over a compact Riemann surface was studied by Atiyah and Bott using tools of differential geometry and algebraic topology: they found generators of that ring and computed its Poincaré series. In joint work with Chiu-Chu Melissa Liu, we study in a similar way the mod 2 cohomology ring of the moduli stack of real vector bundles of fixed topological type over a compact Riemann surface with real structure. The goal of the talk is to explain the principle of that computation, emphasizing the analogies and differences between the real and complex cases, and discuss applications of the method. In particular, we provide explicit generators of mod 2 cohomology rings of moduli stacks of vector bundles over a real algebraic curve.

The rational cohomology ring of the moduli stack of holomorphic vector bundles of fixed rank and degree over a compact Riemann surface was studied by Atiyah and Bott using tools of differential geometry and algebraic topology: they found generators of that ring and computed its Poincaré series. In joint work with Chiu-Chu Melissa Liu, we study in a similar way the mod 2 cohomology ring of the moduli stack of real vector bundles of fixed topological type over a compact Riemann surface with real structure. The goal of the talk is to explain the principle of that computation, emphasizing the analogies and differences between the real and complex cases, and discuss applications of the method. In particular, we provide explicit generators of mod 2 cohomology rings of moduli stacks of vector bundles over a real algebraic curve.

#### Algebraic Geometry Seminar

13:00-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Construction of non-Kähler Calabi-Yau 3-folds by smoothing normal crossing varieties (TBA)

**Taro Sano**(Kobe university)Construction of non-Kähler Calabi-Yau 3-folds by smoothing normal crossing varieties (TBA)

[ Abstract ]

It is an open problem whether there are only finitely many diffeomorphism types of projective Calabi-Yau 3-folds. Kawamata--Namikawa developed log deformation theory of normal crossing Calabi-Yau varieties. As an application of their result, one can construct examples of Calabi-Yau manifolds by smoothing SNC varieties. In this talk, I will explain how to construct examples of non-Kähler Calabi-Yau 3-folds with arbitrarily large 2nd Betti numbers. If time permits, I will also explain an example of involutions on a family of K3 surfaces which do not lift biregularly to the total space. This is based on joint work with Kenji Hashimoto.

It is an open problem whether there are only finitely many diffeomorphism types of projective Calabi-Yau 3-folds. Kawamata--Namikawa developed log deformation theory of normal crossing Calabi-Yau varieties. As an application of their result, one can construct examples of Calabi-Yau manifolds by smoothing SNC varieties. In this talk, I will explain how to construct examples of non-Kähler Calabi-Yau 3-folds with arbitrarily large 2nd Betti numbers. If time permits, I will also explain an example of involutions on a family of K3 surfaces which do not lift biregularly to the total space. This is based on joint work with Kenji Hashimoto.

### 2019/07/08

#### Numerical Analysis Seminar

16:50-18:20 Room #056 (Graduate School of Math. Sci. Bldg.)

Parameter estimation and discretization errors for ordinary differential models (Japanese)

**Takeru Matsuda**(University of Tokyo)Parameter estimation and discretization errors for ordinary differential models (Japanese)

#### Seminar on Geometric Complex Analysis

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

A Riemann-Roch theorem on a weighted infinite graph (Japanese)

**Hiroshi Kaneko**(Tokyo University of Science)A Riemann-Roch theorem on a weighted infinite graph (Japanese)

[ Abstract ]

A Riemann-Roch theorem on a connected finite graph was initiated by M. Baker and S. Norine, where connected graph with finite vertices was investigated and unit weight was given on each edge and vertex of the graph. Since a counterpart of the lowest exponents of the complex variable in the Laurent series was proposed as divisor for the Riemann-Roch theorem on graph, its relationships with tropical geometry were highlighted earlier than other complex analytical observations on graphs. On the other hand, M. Baker and F. Shokrieh revealed tight relationships between chip-firing games and potential theory on graphs, by characterizing reduced divisors on graphs as the solution to an energy minimization problem. The objective of this talk is to establish a Riemann-Roch theorem on an edge-weighted infinite graph. We introduce vertex weight assigned by the given weights of adjacent edges other than the units for expression of divisors and assume finiteness of total mass of graph. This is a joint work with A. Atsuji.

A Riemann-Roch theorem on a connected finite graph was initiated by M. Baker and S. Norine, where connected graph with finite vertices was investigated and unit weight was given on each edge and vertex of the graph. Since a counterpart of the lowest exponents of the complex variable in the Laurent series was proposed as divisor for the Riemann-Roch theorem on graph, its relationships with tropical geometry were highlighted earlier than other complex analytical observations on graphs. On the other hand, M. Baker and F. Shokrieh revealed tight relationships between chip-firing games and potential theory on graphs, by characterizing reduced divisors on graphs as the solution to an energy minimization problem. The objective of this talk is to establish a Riemann-Roch theorem on an edge-weighted infinite graph. We introduce vertex weight assigned by the given weights of adjacent edges other than the units for expression of divisors and assume finiteness of total mass of graph. This is a joint work with A. Atsuji.

### 2019/07/05

#### Algebraic Geometry Seminar

10:30-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Durfee-type inequality for complete intersection surface singularities

**Makoto Enokizono**(Tokyo university of science)Durfee-type inequality for complete intersection surface singularities

[ Abstract ]

Durfee's negativity conjecture says that the signature of the Milnor fiber of a 2-dimensional isolated complete intersection singularity is always negative. In this talk, I will explain that this conjecture is true (more precisely, the signature is bounded above by the negative number determined by the geometric genus, the embedding dimension and the number of irreducible components of the exceptional set of the minimal resolution) by using the theory of invariants of fibered surfaces. If time permits, I will explain the higher dimensional analogue of Durfee's conjecture for isolated complete intersection singularities.

Durfee's negativity conjecture says that the signature of the Milnor fiber of a 2-dimensional isolated complete intersection singularity is always negative. In this talk, I will explain that this conjecture is true (more precisely, the signature is bounded above by the negative number determined by the geometric genus, the embedding dimension and the number of irreducible components of the exceptional set of the minimal resolution) by using the theory of invariants of fibered surfaces. If time permits, I will explain the higher dimensional analogue of Durfee's conjecture for isolated complete intersection singularities.

### 2019/07/04

#### Information Mathematics Seminar

16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)

Isogeny-Based Cryptography (Japanese)

**Katsuyuki Takashima**(Mitsubishi Electric Co./Kyushu Univ.)Isogeny-Based Cryptography (Japanese)

[ Abstract ]

Explanation of the isogeny-based cryptography

Explanation of the isogeny-based cryptography

### 2019/07/03

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Tensor product decompositions and rigidity of full factors

**Amine Marrakchi**(RIMS, Kyoto University)Tensor product decompositions and rigidity of full factors

#### Number Theory Seminar

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Explicit calculation of values of the regulator maps on a certain type of Kummer surfaces (Japanese)

**Ken Sato**(University of Tokyo)Explicit calculation of values of the regulator maps on a certain type of Kummer surfaces (Japanese)

### 2019/07/02

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Brane coproducts and their applications (JAPANESE)

**Shun Wakatsuki**(The University of Tokyo)Brane coproducts and their applications (JAPANESE)

[ Abstract ]

The loop coproduct is a coproduct on the homology of the free loop space of a Poincaré duality space (or more generally a Gorenstein space). In this talk, I will introduce two kinds of brane coproducts which are generalizations of the loop coproduct to the homology of a sphere space (i.e. the mapping space from a sphere). Their constructions are based on the finiteness of the dimensions of mapping spaces in some sense. As an application, I will show the vanishing of some cup products on sphere spaces by comparing these two brane coproducts. This gives a generalization of a result of Menichi for the case of free loop spaces.

The loop coproduct is a coproduct on the homology of the free loop space of a Poincaré duality space (or more generally a Gorenstein space). In this talk, I will introduce two kinds of brane coproducts which are generalizations of the loop coproduct to the homology of a sphere space (i.e. the mapping space from a sphere). Their constructions are based on the finiteness of the dimensions of mapping spaces in some sense. As an application, I will show the vanishing of some cup products on sphere spaces by comparing these two brane coproducts. This gives a generalization of a result of Menichi for the case of free loop spaces.

### 2019/07/01

#### Seminar on Geometric Complex Analysis

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

BCOV invariant and birational equivalence (English)

**Yeping Zhang**(Kyoto Univ.)BCOV invariant and birational equivalence (English)

[ Abstract ]

Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi-Yau manifolds, which is now called BCOV invariant. Now we consider a pair (X,Y), where X is a Kaehler manifold and $Y ¥subseteq X$ is a canonical divisor. In this talk, we extend the BCOV invariant to such pairs. The extended BCOV invariant is well-behaved under birational equivalence. We expect that these considerations may eventually lead to a positive answer to Yoshikawa's conjecture that the BCOV invariant for Calabi-Yau threefold is a birational invariant.

Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi-Yau manifolds, which is now called BCOV invariant. Now we consider a pair (X,Y), where X is a Kaehler manifold and $Y ¥subseteq X$ is a canonical divisor. In this talk, we extend the BCOV invariant to such pairs. The extended BCOV invariant is well-behaved under birational equivalence. We expect that these considerations may eventually lead to a positive answer to Yoshikawa's conjecture that the BCOV invariant for Calabi-Yau threefold is a birational invariant.

#### Colloquium of mathematical sciences and society

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

#### Numerical Analysis Seminar

16:50-18:20 Room #117 (Graduate School of Math. Sci. Bldg.)

The effect of preventing scale formation by ceramic balls and its effect on the human body (Japanese)

**Hideo Kawarada**(AMSOK)The effect of preventing scale formation by ceramic balls and its effect on the human body (Japanese)

#### Mathematical Biology Seminar

11:00-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Taylor's Law of Fluctuation Scaling

https://www.rockefeller.edu/our-scientists/heads-of-laboratories/940-joel-e-cohen/

**Joel E. Cohen**(The Rockefeller University and Columbia University)Taylor's Law of Fluctuation Scaling

[ Abstract ]

A family of nonnegative random variables is said to obey Taylor's law when the variance is proportional to some power b of the mean. For example, in the family of exponential distributions, if the mean is m, then the variance is m^2, so the family of exponential distributions obeys Taylor's law exactly with b=2. Many stochastic processes and the prime numbers obey Taylor's law (exactly or asymptotically). Thousands of empirical illustrations of Taylor's law have been published in many different fields including ecology, demography, finance (stock and currency trading), cancer biology, genetics, fisheries, forestry, meteorology, agriculture, physics, cell biology, computer network engineering, and number theory. This survey talk will review some empirical and theoretical results and open problems about Taylor's law, including recently proved versions of Taylor's law for nonnegative stable laws with infinite mean.

[ Reference URL ]A family of nonnegative random variables is said to obey Taylor's law when the variance is proportional to some power b of the mean. For example, in the family of exponential distributions, if the mean is m, then the variance is m^2, so the family of exponential distributions obeys Taylor's law exactly with b=2. Many stochastic processes and the prime numbers obey Taylor's law (exactly or asymptotically). Thousands of empirical illustrations of Taylor's law have been published in many different fields including ecology, demography, finance (stock and currency trading), cancer biology, genetics, fisheries, forestry, meteorology, agriculture, physics, cell biology, computer network engineering, and number theory. This survey talk will review some empirical and theoretical results and open problems about Taylor's law, including recently proved versions of Taylor's law for nonnegative stable laws with infinite mean.

https://www.rockefeller.edu/our-scientists/heads-of-laboratories/940-joel-e-cohen/

### 2019/06/28

#### Algebraic Geometry Seminar

15:30-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Rational curves on prime Fano 3-folds (TBA)

**Sho Tanimoto**(Kumamoto)Rational curves on prime Fano 3-folds (TBA)

[ Abstract ]

One of important topics in algebraic geometry is the space of rational curves, e.g., the dimension and the number of components of the moduli spaces of rational curves on an algebraic variety X. One of interesting situations where this question is extensively studied is when X is a Fano variety since in this case X is rationally connected so that it does contain a lots of rational curves. In this talk I will talk about my joint work with Brian Lehmann which settles this problem for most Fano 3-folds of Picard rank 1, e.g., a general quartic 3-fold in P^4, and our approach is inspired by Manin’s conjecture which predicts the asymptotic formula for the counting function of rational points on a Fano variety. In particular we systematically use geometric invariants in Manin’s conjecture which have been studied by many mathematicians including Brian and me.

One of important topics in algebraic geometry is the space of rational curves, e.g., the dimension and the number of components of the moduli spaces of rational curves on an algebraic variety X. One of interesting situations where this question is extensively studied is when X is a Fano variety since in this case X is rationally connected so that it does contain a lots of rational curves. In this talk I will talk about my joint work with Brian Lehmann which settles this problem for most Fano 3-folds of Picard rank 1, e.g., a general quartic 3-fold in P^4, and our approach is inspired by Manin’s conjecture which predicts the asymptotic formula for the counting function of rational points on a Fano variety. In particular we systematically use geometric invariants in Manin’s conjecture which have been studied by many mathematicians including Brian and me.

#### Colloquium

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

### 2019/06/27

#### Information Mathematics Seminar

16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)

The Evolution of Elliptic Curve Cryptography (Japanese)

**Katsuyuki Takashima**(Mitsubishi Electric Co./Kyushu Univ.)The Evolution of Elliptic Curve Cryptography (Japanese)

[ Abstract ]

Explanation of the evolution of elliptic curve cryptography

Explanation of the evolution of elliptic curve cryptography

### 2019/06/26

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

### 2019/06/25

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Geometry of symplectic log Calabi-Yau surfaces (ENGLISH)

**Tian-Jun Li**(University of Minnesota)Geometry of symplectic log Calabi-Yau surfaces (ENGLISH)

[ Abstract ]

This is a survey on the geometry of symplectic log Calabi-Yau surfaces, which are the symplectic analogues of Looijenga pairs. We address the classification up to symplectic deformation, the relations between symplectic circular sequences and anti-canonical sequences, contact trichotomy, and symplectic fillings. This is a joint work with Cheuk Yu Mak.

This is a survey on the geometry of symplectic log Calabi-Yau surfaces, which are the symplectic analogues of Looijenga pairs. We address the classification up to symplectic deformation, the relations between symplectic circular sequences and anti-canonical sequences, contact trichotomy, and symplectic fillings. This is a joint work with Cheuk Yu Mak.

### 2019/06/24

#### Seminar on Geometric Complex Analysis

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

A certain holomorphic invariant and its applications (Japanese)

**Atsushi Yamamori**(Kogakuin University)A certain holomorphic invariant and its applications (Japanese)

[ Abstract ]

In this talk, we first explain a Bergman geometric proof of inequivalence of the unit ball and the bidisk. In this proof, the homogeneity of the domains plays a substantial role. We next explain a recent attempt to extend our method for non-homogeneous cases.

In this talk, we first explain a Bergman geometric proof of inequivalence of the unit ball and the bidisk. In this proof, the homogeneity of the domains plays a substantial role. We next explain a recent attempt to extend our method for non-homogeneous cases.

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