## Colloquium

Title

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Tropical geometry and zeta values
**

Date

2018.7.11 (Wed) 16:30-17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Hiroshi Iritani (Kyoto University)

Title

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On singular stochastic PDEs
**

Date

2018.7.4 (Wed) 16:30-17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Tadahiro Oh (The University of Edinburgh)

Abstract

In recent years, there has been significant progress on theoretical understanding of singular stochastic partial differential equations (SPDEs) with rough random forcing. The main difficulty in studying singular SPDEs lies in making sense of products of distributions, thus giving a precise meaning to an equation after appropriately modifying the equation (via renormalization).

In the field of stochastic parabolic PDEs, M. Hairer introduced the theory of regularity structures and gave a precise meaning to the so-called "subcritical" singular SPDEs such as the KPZ equation and the three-dimensional stochastic quantization equation, for which he was awarded a Fields medal in 2014. Around the same time, M. Gubinelli introduced the theory of paracontrolled distributions and solved a similar class of singular SPDEs. In this talk, I will first go over the basic difficulty in the subject and explain the main idea in these theories. Then, I will discuss recent developments in stochastic dispersive PDEs such as stochastic nonlinear wave and Schrödinger equations along with open problems in the field.

Title

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Modularity in vertex operator algebras
**

Date

2018.6.27 (Wed) 16:30-17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Chongying Dong (RIMS & University of California, Santa Cruz)

Abstract

Modular invariance of characters of a rational conformal field theory has been known since the work of Cardy. It was proved by Zhu that the the space spanned by the irreducible characters of a rational vertex operator algebras is a representation of the full modular group. This representation is a powerful tool in the study of vertex operator algebras and conformal field theory. It conceives many intriguing arithmetic properties, and the Verlinde formula is certainly a notable example. It has been conjectured my people that the kernel of this representation is a congruence subgroup, or the irreducible characters are modular functions on a congruence subgroup. This expository talk will survey our recent proof of this conjecture.

Title

**
Time-series analysis based on delay coordinate - embedding, integral operator, Groebner basis
**

Date

2018.6.20 (Wed) 16:30-17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Naoto Nakano (Kyoto University)

Title

**
Fast reaction limit problems: analysis and applications
**

Date

2018.6.13 (Wed) 16:30-17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Hideki Murakawa (Kyushu University)

Title

**
Maximally writhed real algebraic knots and links
**

Date

2018.6.6 (Wed) 16:30-17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Grigory Mikhalkin (University of Geneva)

Abstract

The Alexander-Briggs tabulation of knots in R^3 (started almost a century ago, and considered as one of the most traditional ones in classical Knot Theory) is based on the minimal number of crossings for a knot diagram. From the point of view of Real Algebraic Geometry it is more natural to consider knots in RP^3 rather than R^3, and also to use a different number also serving as a measure of complexity of a knot: the minimal degree of a real algebraic curve representing the knot.

As it was noticed by Oleg Viro about 20 years ago, the writhe of a knot diagram becomes an invariant of a knot in the real algebraic set-up, and corresponds to a Vassiliev invariant of degree 1. In the talk we'll briefly survey these notions, and consider the knots with the maximal possible writhe for its degree. Surprisingly, it turns out that there is a unique maximally writhed knot in RP^3 for every degree d. Furthermore, this real algebraic knot type has a number of characteristic properties, from the minimal number of diagram crossing points (equal to d(d-3)/2) to the minimal number of transverse intersections with a plane (equal to d-2). Based on a series of joint works with Stepan Orevkov.

[pdf]

Title

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Mathematical aspects of numerical computation
**

Date

2018.5.30 (Wed) 16:30-17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Koya Sakakibara (Kyoto University)

Title

**
An algorithm for weighted linear matroid parity problem
**

Date

2018.5.23 (Wed) 16:30-17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Yusuke Kobayashi (RIMS, Kyoto University)

Title

**
Birational boundedness of algebraic varieties
**

Date

2018.5.16 (Wed) 14:40-15:40

Place

Rm420, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Christopher Hacon (Kyoto University / The University of Utah)

Abstract

Algebraic varieties are geometric objects defined by polynomial equations. The minimal model program (MMP) is an ambitous program that aims to classify algebraic varieties. According to the MMP, there are 3 building blocks: Fano varieties, Calabi-Yau varieties and varieties of general type. In this talk I will recall the general features of the MMP and discuss recent advances in our understanding of Fano varieties and varieties of general type.

Title

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Global dynamics of the nonlinear Schrodinger equation with potential
**

Date

2018.5.16 (Wed) 16:30-17:30

Place

Rm420, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Kenji Nakanishi (RIMS, Kyoto University)

Abstract

Nonlinear dispersive equations describe wave evolution with strong interactions in various physical contexts, such as plasma, superfluid, and water waves. Each equation typically produces many types of solutions, such as scattering, solitons, and blow-up, by competition between the dispersion and the interactions. Recent progress in the space-time analysis, combined with the variational arguments as well as those in the dynamical system and in the spectral theory, has enabled us to study global behavior of large solutions, but the relation between different types is still to be explored.

In this talk, we consider the nonlinear Schrodinger equation in three dimensions with attractive linear potential and nonlinear interaction, as a simple model case with the four typical solutions: scattering, blow-up, stable solitons and unstable solitons. Restricting the solutions by small mass and energy slightly above the first excited states, we can classify them into 9 sets by global behavior. The blow-up solutions are separated from the solutions scattering to the ground states, by an invariant manifold of codimension one, which is around translations of the potential-free ground state. The transverse intersection of the manifold and its time inversion gives the nine-set decomposition. The dynamic transition from the scattering to the blow-up is stable, taking place near the first excited states once and for all.

Title

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Superpolynomials of plane curve singularities and zeta-functions
**

Date

2018.5.9 (Wed) 16:30-17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Ivan Cherednik (University of North Carolina at Chapel Hill)

Abstract

The talk will be about a recent surprising development in the highly interdisciplinary theory of superpolynomials of plane curve singularities, connecting them with the zeta-functions of the corresponding rings over finite fields. The superpolynomials are stable Khovanov-Rozansky polynomials of algebraic links, which conjecturally coincide with the DAHA superpolynomials and those describing the BPS states in string theory. They are also directly related to affine Springer fibers, $p$-adic orbital integrals and Hilbert schemes of plane curve singularities and the complex plane. The zeta-functions are essentially due to Galkin and Stohr (though we will need some generalization), a very classical direction in number theory. Their definition and examples will be provided and we will formulate a positivity conjecture connecting them with Jacobian factors of plane curve singularities (local factors of the compactifeid Jacobians).

Title

**
Normal closures of slope elements of knot groups
**

Date

2018.5.2 (Wed) 16:30-17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Tetsuya Itoh (Kyoto University)

Title

**
A reconfigurable information-flow semantics for functional programs
**

Date

2018.4.25 (Wed) 16:30-17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Koko Muroya (RIMS, Kyoto University & University of Birmingham）

Abstract

We introduce a new semantic framework---dynamic Geometry of Interaction (dynamic GoI)---for functional programming, as a combination of two styles of program semantics: information-flow and graph-rewriting. A program is interpreted as a network (graph), and program evaluation is modelled using information flow on networks that can be dynamically reconfigured at run-time via graph rewriting. Our starting point is a particular instance of the information-flow semantics, which is Girard's Geometry of Interaction (GoI), a semantic framework to interpret proofs in Linear Logic. It is then interleaved with graph rewriting, on the key principle that the dynamic rewriting is guided and controlled by information flow. This talk gives an overview of development of the dynamic GoI framework, with discussion on its ability to model both intensional and extensional aspects of program evaluation.

Title

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Coset construction and quantum geometric Langlands program
**

Date

2018.4.18 (Wed) 16:30-17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Tomoyuki Arakawa (RIMS, Kyoto University)

Abstract

Coset construction is a well-known method to obtain new vertex algebras from known ones. Recently, Davide Gaiotto had started to give new interpretations of coset construction in terms of 4d gauge theories and the geometric Langlands program. In this lecture I first talk about my joint work with Thomas Creutzig and Andrew Linshaw that proves a long-standing conjecture on the coset construction of W-algebras. Then I explain the method used in this work also proves a conjecture of Dennis Gaitsgory that is crucially used in the quantum geometric Langlands program.

Title

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Operator Algebras and Conformal Field Theory
**

Date

2018.4.11 (Wed) 16:30-17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Yasuyuki Kawahigashi (The University of Tokyo)