## Seminar information archive

Seminar information archive ～12/09｜Today's seminar 12/10 | Future seminars 12/11～

### 2013/11/22

#### FMSP Lectures

10:40-11:40 Room #123 (Graduate School of Math. Sci. Bldg.)

Integrable discrete systems, an introduction Pt. 2 (ENGLISH)

**Alfred RAMANI**(École polytechnique)Integrable discrete systems, an introduction Pt. 2 (ENGLISH)

[ Abstract ]

The second part will mostly be devoted to the various integrability detectors (singularity confinement, algebraic entropy) for integrability of discrete systems, in one or more dimensions. The most important systems identified through these detectors, namely the discrete Painlev¥'e equations, will be presented in detail, through a geometric approach.

The second part will mostly be devoted to the various integrability detectors (singularity confinement, algebraic entropy) for integrability of discrete systems, in one or more dimensions. The most important systems identified through these detectors, namely the discrete Painlev¥'e equations, will be presented in detail, through a geometric approach.

### 2013/11/21

#### GCOE Seminars

15:30-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Cyclic covers and toroidal embeddings (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/documents/miniworkshop.pdf

**Florin Ambro**(IMAR)Cyclic covers and toroidal embeddings (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/documents/miniworkshop.pdf

### 2013/11/20

#### Number Theory Seminar

16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)

On the homotopy exact sequence for the logarithmic de Rham fundamental group (ENGLISH)

**Valentina Di Proietto**(The University of Tokyo)On the homotopy exact sequence for the logarithmic de Rham fundamental group (ENGLISH)

[ Abstract ]

Let K be a field of characteristic 0 and let X* be a quasi-projective simple normal crossing log variety over the log point K* associated to K. We construct a log de Rham version of the homotopy sequence \\pi_1(X*/K*)-->\\pi_1(X*/K)--\\pi_1(K*/K)-->1 and prove that it is exact. Moreover we show the injectivity of the first map for certain quotients of the groups. Our proofs are purely algebraic. This is a joint work with A. Shiho.

Let K be a field of characteristic 0 and let X* be a quasi-projective simple normal crossing log variety over the log point K* associated to K. We construct a log de Rham version of the homotopy sequence \\pi_1(X*/K*)-->\\pi_1(X*/K)--\\pi_1(K*/K)-->1 and prove that it is exact. Moreover we show the injectivity of the first map for certain quotients of the groups. Our proofs are purely algebraic. This is a joint work with A. Shiho.

#### Operator Algebra Seminars

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

The spectrum of large random matrices, the non commutative random variables and the distribution of traffics (ENGLISH)

**Camille Male**(Univ. Paris VII)The spectrum of large random matrices, the non commutative random variables and the distribution of traffics (ENGLISH)

#### Seminar on Probability and Statistics

13:30-14:40 Room #052 (Graduate School of Math. Sci. Bldg.)

TD法における価値関数への収束アルゴリズム (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/07.html

**NOMURA, Ryosuke**(Graduate school of Mathematical Sciences, Univ. of Tokyo)TD法における価値関数への収束アルゴリズム (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/07.html

### 2013/11/19

#### Tuesday Seminar on Topology

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

Minimal $C^1$-diffeomorphisms of the circle which admit

measurable fundamental domains (JAPANESE)

**Hiroki Kodama**(The University of Tokyo)Minimal $C^1$-diffeomorphisms of the circle which admit

measurable fundamental domains (JAPANESE)

[ Abstract ]

We construct, for each irrational number $\\alpha$, a minimal

$C^1$-diffeomorphism of the circle with rotation number $\\alpha$

which admits a measurable fundamental domain with respect to

the Lebesgue measure.

This is a joint work with Shigenori Matsumoto (Nihon University).

We construct, for each irrational number $\\alpha$, a minimal

$C^1$-diffeomorphism of the circle with rotation number $\\alpha$

which admits a measurable fundamental domain with respect to

the Lebesgue measure.

This is a joint work with Shigenori Matsumoto (Nihon University).

#### Tuesday Seminar of Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Inverse spectral problem for positive Hankel operators (ENGLISH)

**Alexander Pushnitski**(King's Colledge London)Inverse spectral problem for positive Hankel operators (ENGLISH)

[ Abstract ]

Hankel operators are given by (infinite) matrices with entries

$a_{n+m}$ in $\\ell^2$. We consider inverse spectral problem

for bounded self-adjoint positive Hankel operators.

A famous theorem due to Megretskii, Peller and Treil asserts

that such operators may have any continuous spectrum of

multiplicity one or two and any set of eigenvalues of multiplicity

one. However, more detailed questions of inverse spectral

problem, such as the description of isospectral sets, have never

been addressed. In this talk I will describe in detail the

direct and inverse spectral problem for a particular sub-class

of positive Hankel operators. The talk is based on joint work

with Patrick Gerard (Paris, Orsay).

Hankel operators are given by (infinite) matrices with entries

$a_{n+m}$ in $\\ell^2$. We consider inverse spectral problem

for bounded self-adjoint positive Hankel operators.

A famous theorem due to Megretskii, Peller and Treil asserts

that such operators may have any continuous spectrum of

multiplicity one or two and any set of eigenvalues of multiplicity

one. However, more detailed questions of inverse spectral

problem, such as the description of isospectral sets, have never

been addressed. In this talk I will describe in detail the

direct and inverse spectral problem for a particular sub-class

of positive Hankel operators. The talk is based on joint work

with Patrick Gerard (Paris, Orsay).

#### Lie Groups and Representation Theory

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

Horospheres, wonderfull compactification and c-function (JAPANESE)

**Simon Gindikin**(Rutgers University (USA))Horospheres, wonderfull compactification and c-function (JAPANESE)

[ Abstract ]

I will discuss what is closures of horospheres at the wonderfull compactification and how does it connected with horospherical transforms, c-functions and product-formulas

I will discuss what is closures of horospheres at the wonderfull compactification and how does it connected with horospherical transforms, c-functions and product-formulas

### 2013/11/18

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

無限型リーマン面に対する安定写像類群とモジュライ空間 (JAPANESE)

**Ege Fujikawa**(Chiba University)無限型リーマン面に対する安定写像類群とモジュライ空間 (JAPANESE)

#### FMSP Lectures

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

Integrable discrete systems, an introduction Pt.1 (ENGLISH)

**Alfred RAMANI**(École polytechnique)Integrable discrete systems, an introduction Pt.1 (ENGLISH)

[ Abstract ]

The first part will contain a general overview of the notion of integrability, starting from continuous systems with or without physical applications. The Painlev¥'e property will be discussed as an integrability detector for integrability of continuous systems. The notion of integrability of discrete systems will be introduced next. One dimensional systems will be presented as well as multidimensional ones.

The first part will contain a general overview of the notion of integrability, starting from continuous systems with or without physical applications. The Painlev¥'e property will be discussed as an integrability detector for integrability of continuous systems. The notion of integrability of discrete systems will be introduced next. One dimensional systems will be presented as well as multidimensional ones.

#### Kavli IPMU Komaba Seminar

17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary

(ENGLISH)

**Mauricio Romo**(Kavli IPMU)Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary

(ENGLISH)

[ Abstract ]

I will talk about the recent computation, done in joint work with Prof. K. Hori, of the partition function on the hemisphere of a class of two-dimensional (2,2) supersymmetric field theories including gauged linear sigma models (GLSM). The result provides a general exact formula for the central charge of the D-branes placed at the boundary. From the mathematical point of view, for the case of GLSMs that admit a geometrical interpretation, this formula provides an expression for the central charge of objects in the derived category at any point of the stringy Kahler moduli space. I will describe how this formula arises from physics and give simple, yet important, examples that supports its validity. If time allows, I will also explain some of its consequences such as how it can be used to obtain the grade restriction rule for branes near phase boundaries.

I will talk about the recent computation, done in joint work with Prof. K. Hori, of the partition function on the hemisphere of a class of two-dimensional (2,2) supersymmetric field theories including gauged linear sigma models (GLSM). The result provides a general exact formula for the central charge of the D-branes placed at the boundary. From the mathematical point of view, for the case of GLSMs that admit a geometrical interpretation, this formula provides an expression for the central charge of objects in the derived category at any point of the stringy Kahler moduli space. I will describe how this formula arises from physics and give simple, yet important, examples that supports its validity. If time allows, I will also explain some of its consequences such as how it can be used to obtain the grade restriction rule for branes near phase boundaries.

#### Algebraic Geometry Seminar

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

An injectivity theorem (ENGLISH)

**Florin Ambro**(IMAR)An injectivity theorem (ENGLISH)

[ Abstract ]

I will discuss a generalization of the injectivity theorem of Esnault-Viehweg, and an

application to the problem of lifting sections from the non-log canonical locus of a log variety.

I will discuss a generalization of the injectivity theorem of Esnault-Viehweg, and an

application to the problem of lifting sections from the non-log canonical locus of a log variety.

### 2013/11/16

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Pair correlation of low lying zeros of quadratic L-functions (JAPANESE)

sigam function and space curves (JAPANESE)

**Keijyu SOUNO**(Tokyo University of Agriculture and Technology) 13:30-14:30Pair correlation of low lying zeros of quadratic L-functions (JAPANESE)

[ Abstract ]

In this talk, we give certain asymptotic formula involving non-trivial zeros of L-functions associated to Knonecker symbol under the assumption of the Generalized Riemann Hypothesis. From this formula, we obtain several results on non-trivial zeros of quadratic L-functions near the real axis.

In this talk, we give certain asymptotic formula involving non-trivial zeros of L-functions associated to Knonecker symbol under the assumption of the Generalized Riemann Hypothesis. From this formula, we obtain several results on non-trivial zeros of quadratic L-functions near the real axis.

**Shigeki MATSUTANI**

所属: 相模原(Sagamihara city) 15:30-16:00所属: 相模原

sigam function and space curves (JAPANESE)

[ Abstract ]

In this talk, I show that Kleinian sigma function, which is a generalization of Weierstrass elliptic sigma function, is extended to space curves, (3,4,5), (3,7,8) and (6,13,14,15,16) type. In terms of the function, the Jacobi inversion formula is also generalized, in which the affine coordinates are given as functions of strata of Jacobi variety associated with these curves.

In this talk, I show that Kleinian sigma function, which is a generalization of Weierstrass elliptic sigma function, is extended to space curves, (3,4,5), (3,7,8) and (6,13,14,15,16) type. In terms of the function, the Jacobi inversion formula is also generalized, in which the affine coordinates are given as functions of strata of Jacobi variety associated with these curves.

#### Harmonic Analysis Komaba Seminar

13:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Besov and Triebel-Lizorkin spaces associated with

non-negative self-adjoint operators

(ENGLISH)

On asymptotic behavior of solutions for one-dimensional nonlinear Dirac equation (JAPANESE)

**Guorong Hu**(The University of Tokyo) 13:30-15:00Besov and Triebel-Lizorkin spaces associated with

non-negative self-adjoint operators

(ENGLISH)

[ Abstract ]

Let $(X,d)$ be a locally compact metric space

endowed with a doubling measure $¥mu$, and

let $L$ be a non-negative self-adjoint operator on $L^{2}(X,d¥mu)$.

Assume that the semigroup

$P_{t}=e^{-tL}$

generated by $L$ consists of integral operators with (heat) kernel

$p_{t}(x,y)$

enjoying Gaussian upper bound but having no information on the

regularity in the variables $x$ and $y$.

In this talk, we shall introduce Besov and Triebel-Lizorkin spaces associated

with $L$, and

present an atomic decomposition of these function spaces.

Let $(X,d)$ be a locally compact metric space

endowed with a doubling measure $¥mu$, and

let $L$ be a non-negative self-adjoint operator on $L^{2}(X,d¥mu)$.

Assume that the semigroup

$P_{t}=e^{-tL}$

generated by $L$ consists of integral operators with (heat) kernel

$p_{t}(x,y)$

enjoying Gaussian upper bound but having no information on the

regularity in the variables $x$ and $y$.

In this talk, we shall introduce Besov and Triebel-Lizorkin spaces associated

with $L$, and

present an atomic decomposition of these function spaces.

**Hironobu Sasaki**(Chiba University) 15:30-17:00On asymptotic behavior of solutions for one-dimensional nonlinear Dirac equation (JAPANESE)

### 2013/11/14

#### Geometry Colloquium

10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Homological mirror symmetry of torus fibrations and some deformations (JAPANESE)

**Hiroshige Kajiura**(Chiba University)Homological mirror symmetry of torus fibrations and some deformations (JAPANESE)

[ Abstract ]

We consider pairs of symplectic torus fibrations equipped with foliation structures and noncommutative deformations of complex torus fibrations as some deformations of the formulation of mirror symmetry via torus fibrations by Strominger-Yau-Zaslow. In order to assert that these pairs are mirror dual pairs, we consider homological mirror symmetry. Namely, we define deformations of Fukaya categories on symplectic torus fibrations and deformations of derived categories on complex torus fibrations, and discuss some equivalences between them. (What are known to hold true for non-deformed setting hold true, too, for the deformed setting. )

We consider pairs of symplectic torus fibrations equipped with foliation structures and noncommutative deformations of complex torus fibrations as some deformations of the formulation of mirror symmetry via torus fibrations by Strominger-Yau-Zaslow. In order to assert that these pairs are mirror dual pairs, we consider homological mirror symmetry. Namely, we define deformations of Fukaya categories on symplectic torus fibrations and deformations of derived categories on complex torus fibrations, and discuss some equivalences between them. (What are known to hold true for non-deformed setting hold true, too, for the deformed setting. )

#### Applied Analysis

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Singular limit of a damped wave equation with a bistable nonlinearity (ENGLISH)

**Danielle Hilhorst**(Université de Paris-Sud / CNRS)Singular limit of a damped wave equation with a bistable nonlinearity (ENGLISH)

[ Abstract ]

We study the singular limit of a damped wave equation with

a bistable nonlinearity. In order to understand interfacial

phenomena, we derive estimates for the generation and the motion

of interfaces. We prove that steep interfaces are generated in

a short time and that their motion is governed by mean curvature

flow under the assumption that the damping is sufficiently strong.

To this purpose, we prove a comparison principle for the damped

wave equation and construct suitable sub- and super-solutions.

This is joint work with Mitsunori Nata.

We study the singular limit of a damped wave equation with

a bistable nonlinearity. In order to understand interfacial

phenomena, we derive estimates for the generation and the motion

of interfaces. We prove that steep interfaces are generated in

a short time and that their motion is governed by mean curvature

flow under the assumption that the damping is sufficiently strong.

To this purpose, we prove a comparison principle for the damped

wave equation and construct suitable sub- and super-solutions.

This is joint work with Mitsunori Nata.

### 2013/11/13

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Eigenvalue Constraints and Regularity of Q-tensor Navier-Stokes Dynamics (ENGLISH)

**Mark Wilkinson**(École normale supérieure - Paris)Eigenvalue Constraints and Regularity of Q-tensor Navier-Stokes Dynamics (ENGLISH)

[ Abstract ]

The Q-tensor is a traceless and symmetric 3x3 matrix that describes the small-scale structure in nematic liquid crystals. In order to be physically meaningful, its eigenvalues should be bounded below by -1/3 and above by 2/3. This constraint raises questions regarding the physical predictions of theories which employ the Q-tensor; it also raises analytical issues in both static and dynamic Q-tensor theories of nematic liquid crystals. John Ball and Apala Majumdar recently constructed a singular map on traceless, symmetric matrices that penalises unphysical Q-tensors by giving them an infinite energy cost. In this talk, I shall present some mathematical results for a coupled Navier-Stokes system modelling nematic dynamics into which this map is built, including the existence, regularity and so-called `strict physicality' of its weak solutions.

The Q-tensor is a traceless and symmetric 3x3 matrix that describes the small-scale structure in nematic liquid crystals. In order to be physically meaningful, its eigenvalues should be bounded below by -1/3 and above by 2/3. This constraint raises questions regarding the physical predictions of theories which employ the Q-tensor; it also raises analytical issues in both static and dynamic Q-tensor theories of nematic liquid crystals. John Ball and Apala Majumdar recently constructed a singular map on traceless, symmetric matrices that penalises unphysical Q-tensors by giving them an infinite energy cost. In this talk, I shall present some mathematical results for a coupled Navier-Stokes system modelling nematic dynamics into which this map is built, including the existence, regularity and so-called `strict physicality' of its weak solutions.

#### Number Theory Seminar

18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Goren-Oort stratification and Tate cycles on Hilbert modular varieties (ENGLISH)

**Yichao Tian**(Morningside Center for Mathematics)Goren-Oort stratification and Tate cycles on Hilbert modular varieties (ENGLISH)

[ Abstract ]

Let B be a quaternionic algebra over a totally real field F, and p be a prime at least 3 unramified in F. We consider a Shimura variety X associated to B^* of level prime to p. A generalization of Deligne-Carayol's "modèle étrange" allows us to define an integral model for X. We will then define a Goren-Oort stratification on the characteristic p fiber of X, and show that each closed Goren-Oort stratum is an iterated P^1-fibration over another quaternionic Shimura variety in characteristic p. Now suppose that [F:Q] is even and that p is inert in F. An iteration of this construction gives rise to many algebraic cycles of middle codimension on the characteristic p fibre of Hilbert modular varieties of prime-to-p level. We show that the cohomological classes of these cycles generate a large subspace of the Tate cycles, which, in some special cases, coincides with the prediction of the Tate conjecture for the Hilbert modular variety over finite fields. This is a joint work with Liang Xiao.

Let B be a quaternionic algebra over a totally real field F, and p be a prime at least 3 unramified in F. We consider a Shimura variety X associated to B^* of level prime to p. A generalization of Deligne-Carayol's "modèle étrange" allows us to define an integral model for X. We will then define a Goren-Oort stratification on the characteristic p fiber of X, and show that each closed Goren-Oort stratum is an iterated P^1-fibration over another quaternionic Shimura variety in characteristic p. Now suppose that [F:Q] is even and that p is inert in F. An iteration of this construction gives rise to many algebraic cycles of middle codimension on the characteristic p fibre of Hilbert modular varieties of prime-to-p level. We show that the cohomological classes of these cycles generate a large subspace of the Tate cycles, which, in some special cases, coincides with the prediction of the Tate conjecture for the Hilbert modular variety over finite fields. This is a joint work with Liang Xiao.

#### Operator Algebra Seminars

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Automorphisms of Compact Quantum Groups (ENGLISH)

**Issan Patri**(Inst. Math. Sci.)Automorphisms of Compact Quantum Groups (ENGLISH)

### 2013/11/12

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Optimal initial values and regularity conditions of Besov space type for weak solutions to the Navier-Stokes system (ENGLISH)

**Reinhard Farwig**(Technische Universität Darmstadt)Optimal initial values and regularity conditions of Besov space type for weak solutions to the Navier-Stokes system (ENGLISH)

[ Abstract ]

In a joint work with H. Sohr (Paderborn) and W. Varnhorn (Kassel) we discuss the optimal condition on initial values for the instationary Navier-Stokes system in a bounded domain to get a locally regular solution in Serrin's class.

Then this result based on a description in Besov spaces will be used at all or almost all instants to prove new conditional regularity results for weak solutions.

In a joint work with H. Sohr (Paderborn) and W. Varnhorn (Kassel) we discuss the optimal condition on initial values for the instationary Navier-Stokes system in a bounded domain to get a locally regular solution in Serrin's class.

Then this result based on a description in Besov spaces will be used at all or almost all instants to prove new conditional regularity results for weak solutions.

#### Tuesday Seminar on Topology

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

The Batalin-Vilkovisky Formalism and Cohomology of Moduli Spaces (ENGLISH)

**Alexander Voronov**(University of Minnesota)The Batalin-Vilkovisky Formalism and Cohomology of Moduli Spaces (ENGLISH)

[ Abstract ]

We use the Batalin-Vilkovisky formalism to give a new proof of Costello's theorem on the existence and uniqueness of solution to the Quantum Master Equation. We also make a physically motivated conjecture on the rational homology of moduli spaces. This is a joint work with Domenico D'Alessandro.

We use the Batalin-Vilkovisky formalism to give a new proof of Costello's theorem on the existence and uniqueness of solution to the Quantum Master Equation. We also make a physically motivated conjecture on the rational homology of moduli spaces. This is a joint work with Domenico D'Alessandro.

#### Numerical Analysis Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Numerical analysis of friction-type boundary value problems by "method of numerical integration" (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

**Takahito Kashiwabara**(The University of Tokyo)Numerical analysis of friction-type boundary value problems by "method of numerical integration" (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

### 2013/11/11

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Levi-flat real hypersurfaces with Takeuchi 1-complete complements (JAPANESE)

**Masanori Adachi**(Nagoya University)Levi-flat real hypersurfaces with Takeuchi 1-complete complements (JAPANESE)

[ Abstract ]

In this talk, we discuss compact Levi-flat real hypersurfaces with Takeuchi 1-complete complements from several viewpoints. Based on a Bochner-Hartogs type extension theorem for CR sections over these hypersurfaces, we give an example of a compact Levi-flat CR manifold with a positive CR line bundle whose Ohsawa-Sibony's projective embedding map cannot be transversely infinitely differentiable. We also give a geometrical expression of the Diederich-Fornaess exponents of Takeuchi 1-complete defining functions, and discuss a possible dynamical interpretation of them.

In this talk, we discuss compact Levi-flat real hypersurfaces with Takeuchi 1-complete complements from several viewpoints. Based on a Bochner-Hartogs type extension theorem for CR sections over these hypersurfaces, we give an example of a compact Levi-flat CR manifold with a positive CR line bundle whose Ohsawa-Sibony's projective embedding map cannot be transversely infinitely differentiable. We also give a geometrical expression of the Diederich-Fornaess exponents of Takeuchi 1-complete defining functions, and discuss a possible dynamical interpretation of them.

#### Algebraic Geometry Seminar

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

Geography via the base loci (ENGLISH)

**Sung Rak Choi**(POSTECH)Geography via the base loci (ENGLISH)

[ Abstract ]

The geography of log model refers to the decomposition of the set of effective adjoint divisors into the cells defined by the resulting models that are obtained by the log minimal model program.

We will describe the geography in terms of the asymptotic base loci and Zariski decompositions of divisors.

As an application, we give a partial answer to a question of B. Totaro concerning the structure of partially ample cones.

The geography of log model refers to the decomposition of the set of effective adjoint divisors into the cells defined by the resulting models that are obtained by the log minimal model program.

We will describe the geography in terms of the asymptotic base loci and Zariski decompositions of divisors.

As an application, we give a partial answer to a question of B. Totaro concerning the structure of partially ample cones.

#### Lie Groups and Representation Theory

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

Alternating sign matrices, primed shifted tableaux and Tokuyama

factorisation theorems (ENGLISH)

**Ronald King**(the University of Southampton)Alternating sign matrices, primed shifted tableaux and Tokuyama

factorisation theorems (ENGLISH)

[ Abstract ]

Twenty years ago Okada established a remarkable set of identities relating weighted sums over half-turn alternating sign matrices (ASMs) to products taking the form of deformations of Weyl denominator formulae for Lie algebras B_n, C_n and D_n. Shortly afterwards Simpson added another such identity to the list. It will be shown that various classes of ASMs are in bijective correspondence with certain sets of shifted tableaux, and that statistics on these ASMs may be expressed in terms of the entries in corresponding compass point matrices (CPMs). This then enables the Okada and Simpson identities to be expressed in terms of weighted sums over primed shifted tableaux. This offers the possibility of extending each of these identities, that originally involved a single parameter and a single shifted tableau shape, to more general identities involving both sequences of parameters and shapes specified by arbitrary partitions. It is conjectured that in each case an appropriate multi-parameter weighted sum can be expressed as a product of a deformed Weyl denominator and group character of the type first proved in the A_n case by Tokuyma in 1988. The conjectured forms of the generalised Okada and Simpson identities will be given explicitly, along with an account of recent progress made in collaboration with Angèle Hamel in proving some of them.

Twenty years ago Okada established a remarkable set of identities relating weighted sums over half-turn alternating sign matrices (ASMs) to products taking the form of deformations of Weyl denominator formulae for Lie algebras B_n, C_n and D_n. Shortly afterwards Simpson added another such identity to the list. It will be shown that various classes of ASMs are in bijective correspondence with certain sets of shifted tableaux, and that statistics on these ASMs may be expressed in terms of the entries in corresponding compass point matrices (CPMs). This then enables the Okada and Simpson identities to be expressed in terms of weighted sums over primed shifted tableaux. This offers the possibility of extending each of these identities, that originally involved a single parameter and a single shifted tableau shape, to more general identities involving both sequences of parameters and shapes specified by arbitrary partitions. It is conjectured that in each case an appropriate multi-parameter weighted sum can be expressed as a product of a deformed Weyl denominator and group character of the type first proved in the A_n case by Tokuyma in 1988. The conjectured forms of the generalised Okada and Simpson identities will be given explicitly, along with an account of recent progress made in collaboration with Angèle Hamel in proving some of them.

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