## Seminar information archive

Seminar information archive ～08/23｜Today's seminar 08/24 | Future seminars 08/25～

### 2019/08/20

#### thesis presentations

13:45-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)

### 2019/08/19

#### Numerical Analysis Seminar

13:00-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Staggered hybridisation for discontinuous Galerkin methods (英語)

DG and HDG methods for the variational inequality problems (英語)

A new HDG method using a hybridized flux (英語)

Numerical approximation of the Stokes–Darcy problem using discontinuous linear elements (英語)

**Eric Chung**(The Chinese University of Hong Kong) 13:00-14:00Staggered hybridisation for discontinuous Galerkin methods (英語)

[ Abstract ]

In this talk, we present a new staggered hybridization technique for discontinuous Galerkin methods to discretize linear elastodynamic equations and nonlinear Stokes equations. The idea of hybridization is used extensively in many discontinuous Galerkin methods, but the idea of staggered hybridization is new. Our new approach offers several advantages, namely energy conservation, high-order optimal convergence, preservation of symmetry for the stress tensor, block diagonal mass matrices as well as low dispersion error. The key idea is to use two staggered hybrid variables to enforce the continuity of the velocity and the continuity of the normal component of the stress tensor on a staggered mesh. We prove the stability and the convergence of the proposed scheme in both the semi-discrete and the fully-discrete settings. Numerical results confirm the optimal rate of convergence and show that the method has a superconvergent property for dispersion.

In this talk, we present a new staggered hybridization technique for discontinuous Galerkin methods to discretize linear elastodynamic equations and nonlinear Stokes equations. The idea of hybridization is used extensively in many discontinuous Galerkin methods, but the idea of staggered hybridization is new. Our new approach offers several advantages, namely energy conservation, high-order optimal convergence, preservation of symmetry for the stress tensor, block diagonal mass matrices as well as low dispersion error. The key idea is to use two staggered hybrid variables to enforce the continuity of the velocity and the continuity of the normal component of the stress tensor on a staggered mesh. We prove the stability and the convergence of the proposed scheme in both the semi-discrete and the fully-discrete settings. Numerical results confirm the optimal rate of convergence and show that the method has a superconvergent property for dispersion.

**Feifei Jing**(Northwestern Polytechnical University) 14:30-15:30DG and HDG methods for the variational inequality problems (英語)

[ Abstract ]

There exist many numerical methods for solving the fluid dynamics equations, the main difference between them lies in the partitions of geometric domain and the discrete forms of governing equations. Due to the discontinuous piecewise polynomial subspaces, DG and HDG methods can be easily implemented on highly unstructured meshes, e.g. general polygonal mesh, and volume integrals could be calculated on physical elements, without reference elements and mappings between physical and reference elements. In this talk, DG and HDG methods employed to a class of variational inequality problems arising in hydrodynamics are studied. Some theoretical results will be shown, as well as the implementations of these methods are also put into practice.

There exist many numerical methods for solving the fluid dynamics equations, the main difference between them lies in the partitions of geometric domain and the discrete forms of governing equations. Due to the discontinuous piecewise polynomial subspaces, DG and HDG methods can be easily implemented on highly unstructured meshes, e.g. general polygonal mesh, and volume integrals could be calculated on physical elements, without reference elements and mappings between physical and reference elements. In this talk, DG and HDG methods employed to a class of variational inequality problems arising in hydrodynamics are studied. Some theoretical results will be shown, as well as the implementations of these methods are also put into practice.

**Issei Oikawa**(Hitotsubashi University) 16:00-16:30A new HDG method using a hybridized flux (英語)

[ Abstract ]

We propose a new hybridizable discontinuous Galerkin (HDG) method for steady-state diffusion problems. In our method, both the trace and flux of the exact solution are hybridized. The Lehrenfeld-Schöberl stabilization is implicitly included in the method, so that the orders of convergence in all variables are optimal without postprocessing and computation of any projection. Numerical results are present to show the validation of our method.

We propose a new hybridizable discontinuous Galerkin (HDG) method for steady-state diffusion problems. In our method, both the trace and flux of the exact solution are hybridized. The Lehrenfeld-Schöberl stabilization is implicitly included in the method, so that the orders of convergence in all variables are optimal without postprocessing and computation of any projection. Numerical results are present to show the validation of our method.

**Takahito Kashiwabara**(The University of Tokyo) 16:30-17:00Numerical approximation of the Stokes–Darcy problem using discontinuous linear elements (英語)

[ Abstract ]

We consider the Stokes–Darcy interface problem supplemented with the Beavers– Joseph–Saffman condition on the interface separating two domains. This condition allows for discontinuity in the tangential velocities and in the pressures along the interface. To effectively express it, we propose to use discontinuous linear finite elements to approximate all of the velocities/pressures in the Stokes/Darcy regions. The continuity of velocity in the normal direction is weakly enforced by adopting either the penalty method or Nitsche’s method. We present stability and error estimates for the proposed scheme, taking into account the situation where a curved interface is approximated by a polygonal curve or polyhedral surface.

We consider the Stokes–Darcy interface problem supplemented with the Beavers– Joseph–Saffman condition on the interface separating two domains. This condition allows for discontinuity in the tangential velocities and in the pressures along the interface. To effectively express it, we propose to use discontinuous linear finite elements to approximate all of the velocities/pressures in the Stokes/Darcy regions. The continuity of velocity in the normal direction is weakly enforced by adopting either the penalty method or Nitsche’s method. We present stability and error estimates for the proposed scheme, taking into account the situation where a curved interface is approximated by a polygonal curve or polyhedral surface.

### 2019/08/01

#### Mathematical Biology Seminar

15:00-16:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Mathematical study of the inhibitory role of regulatory T cells in tumor immune response

**Yueping Dong**(Central China Normal University)Mathematical study of the inhibitory role of regulatory T cells in tumor immune response

[ Abstract ]

The immune system against tumor is a complex dynamical process showing a dual role. On the one hand, the immune system can activate some immune cells to kill tumor cells, such as cytotoxic T lymphocytes (CTLs) and natural killer cells (NKs), but on the other hand, more evidence shows that some immune cells can help tumor escape, such as regulatory T cells (Tregs). In this talk, we propose a tumor immune interaction model based on Tregs mediated tumor immune escape mechanism. When HTCs stimulation rate by the presence of identified tumor antigens below the critical value, the interior equilibrium P* is always stable in the region of existence. When HTCs stimulation rate higher than the critical value, the Inhibition rate of ECs by Tregs can destabilize P* and cause Hopf bifurcations and produce limit cycle. This model shows that Tregs might play a crucial role in triggering the immune escape of tumor cells. Furthermore, we introduce the adoptive cellular immunotherapy (ACI) and monoclonal immunotherapy as the treatment to boost the immune system to fight against tumors. The numerical results show that ACI can control more tumor cells, while monoclonal immunotherapy can delay the inhibitory effect of Tregs on effector cells (ECs). The results also show that the combination immunotherapy can control tumor cells and reduce the inhibitory effect of Tregs better than single immunotherapy.

The immune system against tumor is a complex dynamical process showing a dual role. On the one hand, the immune system can activate some immune cells to kill tumor cells, such as cytotoxic T lymphocytes (CTLs) and natural killer cells (NKs), but on the other hand, more evidence shows that some immune cells can help tumor escape, such as regulatory T cells (Tregs). In this talk, we propose a tumor immune interaction model based on Tregs mediated tumor immune escape mechanism. When HTCs stimulation rate by the presence of identified tumor antigens below the critical value, the interior equilibrium P* is always stable in the region of existence. When HTCs stimulation rate higher than the critical value, the Inhibition rate of ECs by Tregs can destabilize P* and cause Hopf bifurcations and produce limit cycle. This model shows that Tregs might play a crucial role in triggering the immune escape of tumor cells. Furthermore, we introduce the adoptive cellular immunotherapy (ACI) and monoclonal immunotherapy as the treatment to boost the immune system to fight against tumors. The numerical results show that ACI can control more tumor cells, while monoclonal immunotherapy can delay the inhibitory effect of Tregs on effector cells (ECs). The results also show that the combination immunotherapy can control tumor cells and reduce the inhibitory effect of Tregs better than single immunotherapy.

### 2019/07/25

#### Operator Algebra Seminars

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

The classification of well behaved simple C*-algebras

**George Elliott**(Univ. Toronto)The classification of well behaved simple C*-algebras

### 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.)

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