Colloquium
RIMS-IMI Colloquium
Title
Lattice and Isogeny Algorithms and Their Applications to Post-Quantum Cryptography
Date
2017.2.1 (Wed) 16:10~17:10 (15:40- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Katsuyuki Takashima (Mitsubishi Electric)
Abstract
Recently, developing post-quantum cryptosystems has been an active research area for preparing emergence (or large deployment) of quantum computers. I will introduce lattice-based and isogeny-based cryptosystems in this talk. Shor's algorithm solves factoring and discrete-logarithm problems in quantum polynomial time. Moreover, the quantum algorithm efficiently solves a wide range of hidden subgroup problems in abelian groups. Therefore, we need mathematical structures, computational assumptions and cryptographic constructions on the structures to avoid the powerful attack. I will survey how to use lattices and isogenies for the purpose.
Title
Singular fibers of stable maps and their applications
Date
2017.2.1 (Wed) 17:40~18:40 (17:10- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Osamu Saeki (IMI, Kyushu University)
Title
Stability and bifurcation analysis of the compressible Navier-Stokes equations
Date
2017.1.25 (Wed) 15:00~16:00
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Yoshiyuki Kagei (Kyushu University)
Title
Analytic K-theory of rigid spaces
Date
2017.1.25 (Wed) 16:40~17:40
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Shuji Saito (Tokyo Institute of Technology)
Abstract
Title
Fargues' conjecture on geometrization of the local Langlands correspondence
Date
2017.1.18 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Naoki Imai (The University of Tokyo)
Title
Rigidity and quasi-invariance for determinantal point processes
Date
2017.1.17 (Tue) 17:00~18:00 (16:30- tea)
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Tomoyuki Shirai (IMI, Kyushu University)
Title
Higher dimensional generalization of Iwasawa theory and related problems
Date
2017.1.11 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Tadashi Ochiai (Osaka University)
Title
On motivic cohomology with compact support
Date
2016.12.14 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Kanetomo Sato (Chuo University)
Title
Some recent developments of an $L^2$ extension theorem
Date
2016.12.7 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Takeo Ohsawa (Nagoya University)
Title
Birational type of orthogonal modular varieties
Date
2016.11.30 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Shohei Ma (Tokyo Institute of Technology)
Title
The reduction modulo p of crystalline representations and hypergeometric polynomials
Date
2016.11.16 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Go Yamashita (RIMS, Kyoto University)
Title
A journey into the theory of computable structures
Date
2016.11.9 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Bakhadyr Khoussainov (RIMS & The University of Auckland, Department of Computer Science)
Abstract
In this talk we introduce the concept of computable structure(such as computable group, graph, algebra, partial order, etc.). We present motivation of the subject, discuss its history, and explain topics and questions that have developed the subject over many years. We explain the role of computability, logic, and algebra in the study of various computable structures. The talk will be informal, non-technical, will contain a good amount of examples and explanations, and accessible to a general mathematics and computer science audience.
Title
Modern Abstract Mathematics at Work: Disentangling Complex Computer Systems with Category Theory and Logic
Date
2016.11.2 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Ichiro Hasuo (The University of Tokyo)
Title
Models of torsors under elliptic curves
Date
2016.10.26 (Wed) 15:00~16:00 (16:00- tea)
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Kentaro Mitsui (Kobe University)
Abstract
We classify reductions of torsors (principal homogeneous spaces) under elliptic curves over a complete discrete valuation field with perfect residue field. Models of such torsors are analogues of elliptic fibrations over a disk. As an application, we show that there exists a separable closed point of small degree on such a torsor.
Title
Normalized entropy versus volume for pseudo-Anosovs
Date
2016.10.26 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Sadayoshi Kojima (Tokyo Institute of Technology)
Abstract
We show that the ratio of the normalized entropy of pseudo-Anosovs of surfaces to the volume of their mapping tori is bounded from below by a positive constant not depending on the topology of surfaces, and then discuss a few of its corollaries.
Title
Recent cryptology and mathematics
Date
2016.10.19 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Koji Nuida (AIST ⁄ JST PRESTO)
Title
Arithmetics of determinantal representations of plane cubics
Date
2016.10.12 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm127, Building No.3, Faculty of Science, Kyoto University
Speaker
Yasuhiro Ishitsuka (Kyoto University)
Title
Isothermal two-phase flows with phase transitions
Date
2016.10.5 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Senjo Shimizu (Kyoto University)
Title
Del Pezzo surfaces and exceptional groups
Date
2016.7.20 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Nicholas Shepherd-Barron (King's College London)
Abstract
The configuration of lines on a del Pezzo surface, such as a cubic surface, leads to various root data, which lead in turn to simple algebraic groups. After reviewing these constructions, we show how to invert the process, by passing in a direct geometrical way from the group to the surface. This inverse construction, which is joint work with Grojnowski, is motivated by boundary phenomena for moduli of K3 surfaces.
Title
Global instability of solutions for drift-diffusion equations in higher dimensions
Date
2016.7.13 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Takayoshi Ogawa (Tohoku University)
Title
Motives and heights
Date
2016.7.6 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Teruhisa Koshikawa (RIMS, Kyoto University)
Title
LOGSPACE vs. PTIME
Date
2016.6.29 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Kazuo Iwama (RIMS, Kyoto University)
Abstract
The famous P vs. NP question asks whether the class of problems that can be solved in polynomial time is different from the class of problems that can be solved in polynomial time if we are given a ``witness''. This super famous open question hides many other open questions about the hierarchy of complexity classes, including the equally important question on the possible difference between logarithmic space and polynomial time. This is the main topic of this talk: Toward the ultimate goal of separating those classes, the problem called the tree evaluation problem was recently introduced. In this talk, we study why this problem is important for our goal and as its first step, we obtain a certain lower bound on its computational complexity using the computation model called branching programs.
Title
The homotopy type of spaces of resultants and related topics
Date
2016.6.22 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Kohhei Yamaguchi (The University of Electro-Communications)
Abstract
Title
Applications of algebraic D-modules to projective varieites.
Date
2016.6.15 (Wed) 14:40~15:40
Place
Rm420, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Robin Hartshorne (University of California, Berkeley)
Abstract
Title
Quantum scattering in time-periodic electromagnetic fields
Date
2016.6.15 (Wed) 16:30~17:30
Place
Rm420, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Tadayoshi Adachi (Kyoto University)
Title
Transition to turbulence in subcritical flows: dynamical systems and beyond
Date
2016.6.8 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Paul Manneville 氏 (RIMS & École polytechnique)
Abstract
Understanding the transition to turbulence at a concrete level has great importance both conceptually and practically. Once put in the realm of dynamical systems theory by Ruelle and Takens (1971), the problem can be considered as essentially solved for systems like Rayleigh-Bénard convection experiencing a progressive and continuous, globally supercritical growth of disorder. For open flows, difficulties arise when there is no relevant linear instability mechanism to explain the wilder form of transition to turbulence that then takes place via coexisting domains of laminar and turbulent flow. I will give a brief overview of the situation and discuss the currently developed paths followed to improve our understanding, from the search for exact solutions of the Navier-Stokes equations within dynamical systems theory to tentative modeling in terms of stochastic systems of use in statistical physics.
Title
Integrated version of Varadhan's asymptotics for first-order perturbations of strong local Dirichlet forms
Date
2016.6.1 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Masanori Hino (Kyoto University)
Title
Intrinsic Diophantine approximation on homogenous algebraic varieties
Date
2016.5.25 (Wed) 15:00~16:00 (16:00- tea)
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Amos Nevo (Technion)
Abstract
We will describe a recently developed general approach to the problem of intrinsic Diophantine approximation on homogeneous algebraic varieties, raised by Serge Lang in 1965, and demonstrate it in many natural examples. The approach utilizes harmonic analysis in the automorphic representation associated with a lattice in an algebraic group, together with some arguments in homogeneous dynamics and ergodic theory. It provides the best possible solution to some previously inaccessible intrinsic Diophantine approximation problems, and raises some challenging open problems in others.
Based on joint work with Anish Ghosh and Alex Gorodnik.
Title
Random walks on (hyperbolic) groups
Date
2016.5.25 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Pierre Mathieu (RIMS & Université d'Aix-Marseille)
Abstract
The first part of the talk will be an introduction to the general theory of random walks on groups with some classical results on entropy, rate of escape ... . For hyperbolic groups, these probabilistic objects have geometric counterparts in terms of Gromov boundary, quasi-conformal measures ... I will mention applications and open questions. Finally I will discuss fluctuation results - like the central limit theorem - in particular a recent work with A. Sisto on deviation inequalities for random walks on cylindrically hyperbolic groups.
Title
On an algebro-geometric realization of the cohomology ring of conical symplectic resolutions
Date
2016.5.11 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Tatsuyuki Hikita (RIMS, Kyoto University)
Title
On viscous incompressible flows around a rotating obstacle in two-dimensions
Date
2016.4.27 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Building No.3, Faculty of Science, Kyoto University
Speaker
Yasunori Maekawa (Kyoto University)
Title
Towards criteria for K-stability of Fano manifolds
Date
2016.4.20 (Wed) 16:30~17:30 (16:00- tea)
Place
Rm110, Research Institute for Mathematical Sciences, Kyoto University
Speaker
Kento Fujita (RIMS, Kyoto University)
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