## Seminar information archive

Seminar information archive ～08/17｜Today's seminar 08/18 | Future seminars 08/19～

#### Tuesday Seminar on Topology

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

Independence of Roseman moves for surface-knot diagrams (JAPANESE)

**Kokoro Tanaka**(Tokyo Gakugei University)Independence of Roseman moves for surface-knot diagrams (JAPANESE)

[ Abstract ]

Roseman moves are seven types of local modifications for surface-knot diagrams in 3-space which generate ambient isotopies of surface-knots in 4-space. In this talk, I will discuss independence among the seven Roseman moves. In particular, I will focus on Roseman moves involving triple points and on those involving branch points. The former is joint work with Kanako Oshiro (Sophia University) and Kengo Kawamura (Osaka City University), and the latter is joint work with Masamichi Takase (Seikei University).

Roseman moves are seven types of local modifications for surface-knot diagrams in 3-space which generate ambient isotopies of surface-knots in 4-space. In this talk, I will discuss independence among the seven Roseman moves. In particular, I will focus on Roseman moves involving triple points and on those involving branch points. The former is joint work with Kanako Oshiro (Sophia University) and Kengo Kawamura (Osaka City University), and the latter is joint work with Masamichi Takase (Seikei University).

### 2016/05/23

#### Seminar on Geometric Complex Analysis

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

A computation method for algebraic local cohomology and its applications (JAPANESE)

**Katsusuke Nabeshima**(The University of Tokushima)A computation method for algebraic local cohomology and its applications (JAPANESE)

[ Abstract ]

Local cohomology was introduced by A. Grothendieck. Subsequent development to a great extent has been motivated by Grothendieck's ideas. Nowadays, local cohomology is a key ingredient in algebraic geometry, commutative algebra, topology and D-modules, and is a fundamental tool for applications in several fields.

In this talk, an algorithmic method to compute algebraic local cohomology classes (with parameters), supported at a point, associated with a given zero-dimensional ideal, is considered in the context of symbolic computation. There are several applications of the method. For example, the method can be used to analyze properties of singularities and deformations of Artin algebra. As the applications, methods for computing standard bases of zero-dimensional ideals and solving ideal membership problems, are also introduced.

Local cohomology was introduced by A. Grothendieck. Subsequent development to a great extent has been motivated by Grothendieck's ideas. Nowadays, local cohomology is a key ingredient in algebraic geometry, commutative algebra, topology and D-modules, and is a fundamental tool for applications in several fields.

In this talk, an algorithmic method to compute algebraic local cohomology classes (with parameters), supported at a point, associated with a given zero-dimensional ideal, is considered in the context of symbolic computation. There are several applications of the method. For example, the method can be used to analyze properties of singularities and deformations of Artin algebra. As the applications, methods for computing standard bases of zero-dimensional ideals and solving ideal membership problems, are also introduced.

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Sub-Riemannian diffusions on foliated manifolds

**Fabrice Baudoin**(Department of mathematics, Purdue university)Sub-Riemannian diffusions on foliated manifolds

[ Abstract ]

We study the horizontal diffusion of a totally geodesic Riemannian foliation. We particularly focus on integration by parts formulas on the path space of the diffusion and present several heat semigroup gradient bounds as a consequence. Connections with a generalized sub-Riemannian curvature dimension inequality are made.

We study the horizontal diffusion of a totally geodesic Riemannian foliation. We particularly focus on integration by parts formulas on the path space of the diffusion and present several heat semigroup gradient bounds as a consequence. Connections with a generalized sub-Riemannian curvature dimension inequality are made.

#### Numerical Analysis Seminar

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Inner-iteration preconditioning for least squares problems and its applications (日本語)

**Keiichi Morikuni**(University of Tsukuba)Inner-iteration preconditioning for least squares problems and its applications (日本語)

[ Abstract ]

We discuss inner-iteration preconditioning for Krylov subspace methods for solving large-scale linear least squares problems. The preconditioning uses several steps of stationary iterative methods, and is efficient when the successive overrelaxation (SOR) method for the normal equations is employed. The SOR inner-iteration left/right-preconditioned generalized minimal residual (BA/AB-GMRES) methods determine a least squares solution/the minimum-norm solution of linear systems of equations without breakdown even in the rank-deficient case. The inner-iteration preconditioning requires less memory than incomplete matrix factorization-type one, and is effective for ill-conditioned and/or rank-deficient least squares problems.

We present applications of inner-iteration preconditioning to solutions of (1) general least squares problems, which is to find a least squares solution whose Euclidean norm is minimum; (2) linear systems of equations which arise in an interior-point method for solving linear programming problems. In (1), we focus on a two-step procedure for the solution of general least squares problems; the first step is to determine a least squares solution and the second step is to determine the minimum-norm solution to a linear system of equation. The solution of each step can be done by using the inner-iteration preconditioned GMRES methods. Numerical experiments show that the SOR inner-iteration preconditioned GMRES methods are more efficient than previous methods for some problems. In (2), the linear systems of equations at each interior-point step become ill-conditioned in the late phase of the interior-point iterations. To solve the linear systems of equation robustly, the inner-iteration preconditioning applies. We present efficient techniques to apply the inner-iteration preconditioning to the linear systems of equations. Numerical experiments on benchmark problems show that the inner-iteration preconditioning is robust compared to previous methods. (2) is joint work with Yiran Cui (University College London), Takashi Tsuchiya (National Graduate Institute for Policy Studies) , and Ken Hayami (National Institute of Informatics and SOKENDAI).

We discuss inner-iteration preconditioning for Krylov subspace methods for solving large-scale linear least squares problems. The preconditioning uses several steps of stationary iterative methods, and is efficient when the successive overrelaxation (SOR) method for the normal equations is employed. The SOR inner-iteration left/right-preconditioned generalized minimal residual (BA/AB-GMRES) methods determine a least squares solution/the minimum-norm solution of linear systems of equations without breakdown even in the rank-deficient case. The inner-iteration preconditioning requires less memory than incomplete matrix factorization-type one, and is effective for ill-conditioned and/or rank-deficient least squares problems.

We present applications of inner-iteration preconditioning to solutions of (1) general least squares problems, which is to find a least squares solution whose Euclidean norm is minimum; (2) linear systems of equations which arise in an interior-point method for solving linear programming problems. In (1), we focus on a two-step procedure for the solution of general least squares problems; the first step is to determine a least squares solution and the second step is to determine the minimum-norm solution to a linear system of equation. The solution of each step can be done by using the inner-iteration preconditioned GMRES methods. Numerical experiments show that the SOR inner-iteration preconditioned GMRES methods are more efficient than previous methods for some problems. In (2), the linear systems of equations at each interior-point step become ill-conditioned in the late phase of the interior-point iterations. To solve the linear systems of equation robustly, the inner-iteration preconditioning applies. We present efficient techniques to apply the inner-iteration preconditioning to the linear systems of equations. Numerical experiments on benchmark problems show that the inner-iteration preconditioning is robust compared to previous methods. (2) is joint work with Yiran Cui (University College London), Takashi Tsuchiya (National Graduate Institute for Policy Studies) , and Ken Hayami (National Institute of Informatics and SOKENDAI).

### 2016/05/18

#### Number Theory Seminar

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

A consequence of Greenberg's generalized conjecture on Iwasawa invariants of Z_p-extensions (Japanese)

**Takenori Kataoka**(University of Tokyo)A consequence of Greenberg's generalized conjecture on Iwasawa invariants of Z_p-extensions (Japanese)

### 2016/05/17

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

On dual defects of toric varieties (TBA)

https://sites.google.com/site/atsushiito221/

**Atsushi Ito**(Dep. of Math. Kyoto Univ. )On dual defects of toric varieties (TBA)

[ Abstract ]

For a projective variety embedded in a projective space,

we can define the dual variety in the dual projective space.

By dimension count, the codimension of the dual variety is expected to be one,

but it can be greater than one for some varieties.

For a smooth toric variety, it is known that the codimension of the dual variety is greater than one

if and only if the toric variety is a suitable projective bundle over some toric variety.

In this talk, I will explain a generalization of this result to toric varieties without the assumption of singularities.

This is a joint work with Katsuhisa Furukawa.

[ Reference URL ]For a projective variety embedded in a projective space,

we can define the dual variety in the dual projective space.

By dimension count, the codimension of the dual variety is expected to be one,

but it can be greater than one for some varieties.

For a smooth toric variety, it is known that the codimension of the dual variety is greater than one

if and only if the toric variety is a suitable projective bundle over some toric variety.

In this talk, I will explain a generalization of this result to toric varieties without the assumption of singularities.

This is a joint work with Katsuhisa Furukawa.

https://sites.google.com/site/atsushiito221/

#### Tuesday Seminar on Topology

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

Some dynamics of random walks on the mapping class groups (JAPANESE)

**Hidetoshi Masai**(The University of Tokyo)Some dynamics of random walks on the mapping class groups (JAPANESE)

[ Abstract ]

The dynamics of random walks on the mapping class groups on closed surfaces of genus >1 will be discussed. We define the topological entropy of random walks. Then we prove that the drift with respect to Thurston or Teichmüller metrics and the Lyapunov exponent all coincide with the topological entropy. This is a "random version" of pseudo-Anosov dynamics observed by Thurston and I will begin this talk by recalling the work of Thurston.

The dynamics of random walks on the mapping class groups on closed surfaces of genus >1 will be discussed. We define the topological entropy of random walks. Then we prove that the drift with respect to Thurston or Teichmüller metrics and the Lyapunov exponent all coincide with the topological entropy. This is a "random version" of pseudo-Anosov dynamics observed by Thurston and I will begin this talk by recalling the work of Thurston.

### 2016/05/16

#### Seminar on Geometric Complex Analysis

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

(JAPANESE)

**Masataka Tomari**(Nihon University)(JAPANESE)

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Generation and propagation of fine transition layers for the Allen-Cahn equation with mild noise

**Hiroshi Matano**(Graduate School of Mathematical Sciences, the university of Tokyocho)Generation and propagation of fine transition layers for the Allen-Cahn equation with mild noise

### 2016/05/11

#### Number Theory Seminar

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

Syntomic complexes and p-adic nearby cycles (English)

**Wiesława Nizioł**(CNRS & ENS de Lyon)Syntomic complexes and p-adic nearby cycles (English)

[ Abstract ]

I will present a proof of a comparison isomorphism, up to some universal constants, between truncated sheaves of p-adic nearby cycles and syntomic cohomology sheaves on semistable schemes over a mixed characteristic local rings. This generalizes the comparison results of Kato, Kurihara, and Tsuji for small Tate twists (where no constants are necessary) as well as the comparison result of Tsuji that holds over the algebraic closure of the field. This is a joint work with Pierre Colmez.

I will present a proof of a comparison isomorphism, up to some universal constants, between truncated sheaves of p-adic nearby cycles and syntomic cohomology sheaves on semistable schemes over a mixed characteristic local rings. This generalizes the comparison results of Kato, Kurihara, and Tsuji for small Tate twists (where no constants are necessary) as well as the comparison result of Tsuji that holds over the algebraic closure of the field. This is a joint work with Pierre Colmez.

### 2016/05/10

#### Tuesday Seminar on Topology

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

On Milnor's link-homotopy invariants for handlebody-links (JAPANESE)

**Yuka Kotorii**(The University of Tokyo)On Milnor's link-homotopy invariants for handlebody-links (JAPANESE)

[ Abstract ]

A handlebody-link is a disjoint union of handlebodies embedded in $S^3$ and HL-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes. A. Mizusawa and R. Nikkuni classified the set of HL-homotopy classes of 2-component handlebody-links completely using the linking numbers for handlebody-links. In this talk, by using Milnor's link-homotopy invariants, we construct an invariant for handlebody-links and give a bijection between the set of HL-homotopy classes of n-component handlebody-links with some assumption and a quotient of the action of the general linear group on a tensor product of modules. This is joint work with Atsuhiko Mizusawa at Waseda University.

A handlebody-link is a disjoint union of handlebodies embedded in $S^3$ and HL-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes. A. Mizusawa and R. Nikkuni classified the set of HL-homotopy classes of 2-component handlebody-links completely using the linking numbers for handlebody-links. In this talk, by using Milnor's link-homotopy invariants, we construct an invariant for handlebody-links and give a bijection between the set of HL-homotopy classes of n-component handlebody-links with some assumption and a quotient of the action of the general linear group on a tensor product of modules. This is joint work with Atsuhiko Mizusawa at Waseda University.

### 2016/05/09

#### Seminar on Geometric Complex Analysis

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

Nevanlinna type theorems for meromorphic functions on negatively curved Kähler manifolds (JAPANESE)

**Atsushi Atsuji**(Keio University)Nevanlinna type theorems for meromorphic functions on negatively curved Kähler manifolds (JAPANESE)

[ Abstract ]

We discuss a generalization of classical Nevanlinna theory to meromorphic functions on complete Kähler manifolds. Several generalization of domains of functions are known in Nevanlinna theory, especially the results due to W.Stoll are well-known. In general Kähler case the remainder term of the second main theorem of Nevanlinna theory usually takes a complicated form. It seems that we have to modify classical

methods in order to simplify the second main theorem. We will use heat diffusion to do that and show some defect relations. We would also like to give some Liouville type theorems for holomorphic maps by using similar heat diffusion methods.

We discuss a generalization of classical Nevanlinna theory to meromorphic functions on complete Kähler manifolds. Several generalization of domains of functions are known in Nevanlinna theory, especially the results due to W.Stoll are well-known. In general Kähler case the remainder term of the second main theorem of Nevanlinna theory usually takes a complicated form. It seems that we have to modify classical

methods in order to simplify the second main theorem. We will use heat diffusion to do that and show some defect relations. We would also like to give some Liouville type theorems for holomorphic maps by using similar heat diffusion methods.

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

**Yosuke Kawamoto**(Graduate school of Mathematics, Kyushu university)#### Numerical Analysis Seminar

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Potential theoretic approach to design of formulas for function approximation and numerical integration in weighted Hardy spaces

(日本語)

**Ken'ichiro Tanaka**(Musashino University)Potential theoretic approach to design of formulas for function approximation and numerical integration in weighted Hardy spaces

(日本語)

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Surgery theory and discrete groups (English)

**Mikael Pichot**(McGill Univ./Univ．Tokyo)Surgery theory and discrete groups (English)

#### FMSP Lectures

15:00-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Vertex Operator Algebras according to Newton (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tuite.pdf

**Michael Tuite**(National University of Ireland, Galway)Vertex Operator Algebras according to Newton (ENGLISH)

[ Abstract ]

In this lecture I will give an introduction to Vertex Operator Algebras (VOAs) using elementary methods originally due to Isaac Newton. I will also discuss a class of exceptional VOAs including the Moonshine module which share a number of fundamental properties in common.

[ Reference URL ]In this lecture I will give an introduction to Vertex Operator Algebras (VOAs) using elementary methods originally due to Isaac Newton. I will also discuss a class of exceptional VOAs including the Moonshine module which share a number of fundamental properties in common.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tuite.pdf

### 2016/04/27

#### PDE Real Analysis Seminar

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

Fourier transform versus Hilbert transform (English)

http://u.math.biu.ac.il/~liflyand/

**Elijah Liflyand**(Bar-Ilan University, Israel)Fourier transform versus Hilbert transform (English)

[ Abstract ]

We present several results in which the interplay between the Fourier transform and the Hilbert transform is of special form and importance.

1. In 50-s (Kahane, Izumi-Tsuchikura, Boas, etc.), the following problem in Fourier Analysis attracted much attention: Let $\{a_k\},$ $k=0,1,2...,$ be the sequence of the Fourier coefficients of the absolutely convergent sine (cosine) Fourier series of a function $f:\mathbb T=[-\pi,\pi)\to \mathbb C,$ that is $\sum |a_k|<\infty.$ Under which conditions on $\{a_k\}$ the re-expansion of $f(t)$ ($f(t)-f(0)$, respectively) in the cosine (sine) Fourier series will also be absolutely convergent?

We solve a similar problem for functions on the whole axis and their Fourier transforms. Generally, the re-expansion of a function with integrable cosine (sine) Fourier transform in the sine (cosine) Fourier transform is integrable if and only if not only the initial Fourier transform is integrable but also the Hilbert transform of the initial Fourier transform is integrable.

2. The following result is due to Hardy and Littlewood: If a (periodic) function $f$ and its conjugate $\widetilde f$ are both of bounded variation, their Fourier series converge absolutely.

We generalize the Hardy-Littlewood theorem (joint work with U. Stadtmüller) to the Fourier transform of a function on the real axis and its modified Hilbert transform. The initial Hardy-Littlewood theorem is a partial case of this extension, when the function is taken to be with compact support.

3. These and other problems are integrated parts of harmonic analysis of functions of bounded variation. We have found the maximal space for the integrability of the Fourier transform of a function of bounded variation. Along with those known earlier, various interesting new spaces appear in this study. Their inter-relations lead, in particular, to improvements of Hardy's inequality.

There are multidimensional generalizations of these results.

[ Reference URL ]We present several results in which the interplay between the Fourier transform and the Hilbert transform is of special form and importance.

1. In 50-s (Kahane, Izumi-Tsuchikura, Boas, etc.), the following problem in Fourier Analysis attracted much attention: Let $\{a_k\},$ $k=0,1,2...,$ be the sequence of the Fourier coefficients of the absolutely convergent sine (cosine) Fourier series of a function $f:\mathbb T=[-\pi,\pi)\to \mathbb C,$ that is $\sum |a_k|<\infty.$ Under which conditions on $\{a_k\}$ the re-expansion of $f(t)$ ($f(t)-f(0)$, respectively) in the cosine (sine) Fourier series will also be absolutely convergent?

We solve a similar problem for functions on the whole axis and their Fourier transforms. Generally, the re-expansion of a function with integrable cosine (sine) Fourier transform in the sine (cosine) Fourier transform is integrable if and only if not only the initial Fourier transform is integrable but also the Hilbert transform of the initial Fourier transform is integrable.

2. The following result is due to Hardy and Littlewood: If a (periodic) function $f$ and its conjugate $\widetilde f$ are both of bounded variation, their Fourier series converge absolutely.

We generalize the Hardy-Littlewood theorem (joint work with U. Stadtmüller) to the Fourier transform of a function on the real axis and its modified Hilbert transform. The initial Hardy-Littlewood theorem is a partial case of this extension, when the function is taken to be with compact support.

3. These and other problems are integrated parts of harmonic analysis of functions of bounded variation. We have found the maximal space for the integrability of the Fourier transform of a function of bounded variation. Along with those known earlier, various interesting new spaces appear in this study. Their inter-relations lead, in particular, to improvements of Hardy's inequality.

There are multidimensional generalizations of these results.

http://u.math.biu.ac.il/~liflyand/

#### Number Theory Seminar

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

On the endoscopic lifting of simple supercuspidal representations (Japanese)

**Masao Oi**(University of Tokyo)On the endoscopic lifting of simple supercuspidal representations (Japanese)

### 2016/04/26

#### Tuesday Seminar of Analysis

16:50-18:20 Room #126 (Graduate School of Math. Sci. Bldg.)

On microlocal analysis of Gauss-Manin connections for boundary singularities (Japanese)

**Saiei-Jaeyeong Matsubara-Heo**(Graduate School of Mathematical Sciences, the University of Tokyo)On microlocal analysis of Gauss-Manin connections for boundary singularities (Japanese)

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

A gentle introduction to K-stability and its recent development (Japanese)

https://sites.google.com/site/yujiodaka2013/

**Yuji Odaka**(Dept. of Math., Kyoto U.)A gentle introduction to K-stability and its recent development (Japanese)

[ Abstract ]

K安定性とは複素代数多様体上の「標準的な」ケーラー計量の存在問題に端を発する，代数幾何的な概念です．二木先生や満渕先生等の先駆的な仕事に感化されて導入され，特に近年ホットに研究され始めている一方，未だその大半はより微分幾何的な研究者の方々や背景の中でなされているように講演者には感じられます．

代数幾何的にもどのように面白いか，どういった意義があるかに私見で軽く触れた上で，その基礎付けをより拡張した枠組みで説明しつつ，最先端でどのようなことが問題になっているかをいくらか（私の力量と時間の許す限り）解説しつつ，文献をご紹介できればと思っています

[ Reference URL ]K安定性とは複素代数多様体上の「標準的な」ケーラー計量の存在問題に端を発する，代数幾何的な概念です．二木先生や満渕先生等の先駆的な仕事に感化されて導入され，特に近年ホットに研究され始めている一方，未だその大半はより微分幾何的な研究者の方々や背景の中でなされているように講演者には感じられます．

代数幾何的にもどのように面白いか，どういった意義があるかに私見で軽く触れた上で，その基礎付けをより拡張した枠組みで説明しつつ，最先端でどのようなことが問題になっているかをいくらか（私の力量と時間の許す限り）解説しつつ，文献をご紹介できればと思っています

https://sites.google.com/site/yujiodaka2013/

#### Tuesday Seminar on Topology

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

Arithmetic topology on branched covers of 3-manifolds (JAPANESE)

**Jun Ueki**(The University of Tokyo)Arithmetic topology on branched covers of 3-manifolds (JAPANESE)

[ Abstract ]

The analogy between 3-dimensional topology and number theory was first pointed out by Mazur in the 1960s, and it has been studied systematically by Kapranov, Reznikov, Morishita, and others. In their analogies, for example, knots and 3-manifolds correspond to primes and number rings respectively. The study of these analogies is called arithmetic topology now.

In my talk, based on their dictionary of analogies, we study analogues of idelic class field theory, Iwasawa theory, and Galois deformation theory in the context of 3-dimensional topology, and establish various foundational analogies in arithmetic topology.

The analogy between 3-dimensional topology and number theory was first pointed out by Mazur in the 1960s, and it has been studied systematically by Kapranov, Reznikov, Morishita, and others. In their analogies, for example, knots and 3-manifolds correspond to primes and number rings respectively. The study of these analogies is called arithmetic topology now.

In my talk, based on their dictionary of analogies, we study analogues of idelic class field theory, Iwasawa theory, and Galois deformation theory in the context of 3-dimensional topology, and establish various foundational analogies in arithmetic topology.

#### Seminar on Probability and Statistics

16:10-17:10 Room #123 (Graduate School of Math. Sci. Bldg.)

LAMN property and optimal estimation for diffusion with non synchronous observations

**Teppei Ogihara**(Institute of Statistical Mathematics, JST PRESTO, JST CREST)LAMN property and optimal estimation for diffusion with non synchronous observations

[ Abstract ]

We study so-called local asymptotic mixed normality (LAMN) property for a statistical model generated by nonsynchronously observed diffusion processes using a Malliavin calculus technique. The LAMN property of the statistical model induces an asymptotic minimal variance of estimation errors for any estimators of the parameter. We also construct an optimal estimator which attains the best asymptotic variance.

We study so-called local asymptotic mixed normality (LAMN) property for a statistical model generated by nonsynchronously observed diffusion processes using a Malliavin calculus technique. The LAMN property of the statistical model induces an asymptotic minimal variance of estimation errors for any estimators of the parameter. We also construct an optimal estimator which attains the best asymptotic variance.

#### Seminar on Probability and Statistics

13:00-14:20 Room #123 (Graduate School of Math. Sci. Bldg.)

Stochastic heat equation with fractional noise 1

**Ciprian Tudor**(Université de Lille 1)Stochastic heat equation with fractional noise 1

[ Abstract ]

In the first part, we introduce the bifractional Brownian motion, which is a Gaussian process that generalizes the well- known fractional Brownian motion. We present the basic properties of this process and we also present its connection with the mild solution to the heat equation driven by a Gaussian noise that behaves as the Brownian motion in time.

In the first part, we introduce the bifractional Brownian motion, which is a Gaussian process that generalizes the well- known fractional Brownian motion. We present the basic properties of this process and we also present its connection with the mild solution to the heat equation driven by a Gaussian noise that behaves as the Brownian motion in time.

#### Seminar on Probability and Statistics

14:30-15:50 Room #123 (Graduate School of Math. Sci. Bldg.)

Stochastic heat equation with fractional noise 2

**Ciprian Tudor**(Université de Lille 1)Stochastic heat equation with fractional noise 2

[ Abstract ]

We will present recent result concerning the heat equation driven by q Gaussian noise which behaves as a fractional Brownian motion in time and has a correlated spatial structure. We give the basic results concerning the existence and the properties of the solution. We will also focus on the distribution of this Gaussian process and its connection with other fractional-type processes.

We will present recent result concerning the heat equation driven by q Gaussian noise which behaves as a fractional Brownian motion in time and has a correlated spatial structure. We give the basic results concerning the existence and the properties of the solution. We will also focus on the distribution of this Gaussian process and its connection with other fractional-type processes.

#### Mathematical Biology Seminar

15:00-16:00 Room #128演習室 (Graduate School of Math. Sci. Bldg.)

Delayed Models of Cancer Dynamics: Lessons Learned in Mathematical Modelling (ENGLISH)

https://web.viu.ca/idelsl/

**Lev Idels**(Vanvouver Island University)Delayed Models of Cancer Dynamics: Lessons Learned in Mathematical Modelling (ENGLISH)

[ Abstract ]

In general, delay differential equations provide a richer mathematical

framework (compared with ordinary differential equations) for the

analysis of biosystems dynamics. The inclusion of explicit time lags in

tumor growth models allows direct reference to experimentally measurable

and/or controllable cell growth characteristics. For three different

types of angiogenesis models with variable delays, we consider either

continuous or impulse therapy that eradicates tumor cells and suppresses

angiogenesis. It was shown that with the growth of delays, even

constant, the equilibrium can lose its stability, and sustainable

oscillation, as well as chaotic behavior, can be observed. The analysis

outlines the difficulties which occur in the case of unbounded growth

rates, such as classical Gompertz model, for small volumes of cancer

cells compared to available blood vessels. The Wheldon model (1975) of a

Chronic Myelogenous Leukemia (CML) dynamics is revisited in the light of

recent discovery that this model has a major drawback.

[ Reference URL ]In general, delay differential equations provide a richer mathematical

framework (compared with ordinary differential equations) for the

analysis of biosystems dynamics. The inclusion of explicit time lags in

tumor growth models allows direct reference to experimentally measurable

and/or controllable cell growth characteristics. For three different

types of angiogenesis models with variable delays, we consider either

continuous or impulse therapy that eradicates tumor cells and suppresses

angiogenesis. It was shown that with the growth of delays, even

constant, the equilibrium can lose its stability, and sustainable

oscillation, as well as chaotic behavior, can be observed. The analysis

outlines the difficulties which occur in the case of unbounded growth

rates, such as classical Gompertz model, for small volumes of cancer

cells compared to available blood vessels. The Wheldon model (1975) of a

Chronic Myelogenous Leukemia (CML) dynamics is revisited in the light of

recent discovery that this model has a major drawback.

https://web.viu.ca/idelsl/

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