一周活动抢先知【6.24-6.30】@中国科学技术大学

数学科学学院

报告题目：On almost semisimple Frobenius manifolds

报告人：王乐维，清华大学

报告时间：2024年6月25日（周二）下午2:00-3:00

报告地点：东区管理科研楼1418教室

报告摘要：In this report, we introduce a class of regular non-semisimple Frobenius manifolds, which we refer to as almost semisimple Frobenius manifolds. We define quasi canonical coordinates on almost semisimple Frobenius manifolds,  use them to analyze the degrees of freedom in the solutions of the loop equations, and provide calculations for several examples.

报告题目：Applications of Floer cohomology to the study of contactomorphisms and Legendrians

报告人：Dylan Cant（迪伦 坎特）（蒙特利尔大学）

报告时间：2024年6月25日 10：00-11：00

报告地点：物质科研楼C1124

报告摘要：In this first talk in a series of two talks, I will briefly review the construction of Floer cohomology for contact-at-infinity Hamiltonian systems and Lagrangians in a convex-at-infinity symplectic manifold W and then discuss its applications to the geometry of the contactomorphisms and Legendrians of the ideal boundary W, including applications to orderability and persistence of translated points and Reeb chords.

报告题目：Monodromy of the higher-order hypergeometric equations I, II

报告人：沈大立（北京雁栖湖应用数学研究院）

报告时间：2024年6月25、27日 16：00-17：30

报告地点：2教2103

报告摘要：In this series of two expository lectures, I will give a brief introduction to the monodromy groups of the higher-order hypergeometric equations, with an emphasis on the determination of their finiteness, arithmeticity or thinness

报告题目：Hassett-Keel program and moduli spaces of Abelian differentials

报告人：于飞（浙江大学）

报告时间：2024年6月26日9：00

报告地点：2教2103

报告摘要：The Hassett-Keel program seeks to offer a modular interpretation for the log minimal model program of the moduli space of stable curves. Alper, Fedorchuk, and Smyth have proposed a conjectural framework for this program by analyzing Gorenstein curve singularities under the action of G_m. Our work draws parallels between this approach and the study of the Kontsevich-Zorich conjectures pertaining to moduli spaces of Abelian differentials. We address pertinent questions in this area by employing test configurations and the Rees construction, methodologies that stem from the theory of K-stability. This research is a collaborative effort with Dawei Chen and is currently in progress.   

腾讯会议：600-3929-5239

https://meeting.tencent.com/dm/Ji5zXJqWY1VB

报告题目：An equivariant approach to contact Floer cohomology

报告人：Dylan Cant（迪伦 坎特）（蒙特利尔大学）

报告时间：2024年6月27日 10：00-11：00

报告地点：物质科研楼C1124

报告摘要：In this second talk, I will discuss some in-progress work concerning an equivariant version of Floer cohomology for contact-at-infinity systems. In particular, I will explain how equivariant methods can be applied to convex-at-infinity manifolds admitting finite group actions to prove rigidity results for contact manifolds such as RPn and some other prequantization spaces.

报告题目：Global well-posedness and ergodicity of 3D Burgers equation with a multiplicative noise force 

报告人：吴奖伦 （香港浸会大学&北京师范大学）

报告时间：6月28日 9:00

报告地点：管理楼1418

报告摘要：This talk is concerned with a 3D Burgers equation perturbed by a linear multiplicative noise. Utilising Doss-Sussman transformation, we link the 3D stochastic Burgers equation to a 3D random Burgers equation. Utilising certain techniques from nonlinear partial differential equations and stochastic analysis, we are able to establish the global well-posedness of 3D Burgers equation with constant diffusion coefficient. Moreover, by developing a solution which is orthogonal to the gradient of diffusion coefficient, we extend the global well-posedness result to a more general case to allow the diffusion coefficient to be a function of space and time variables. Our results and methodology pave a way to extend regularity results of 1D Burgers equations to 3D Burgers equations. Based on joint works with Zhao Dong (Chinese Academy of Sciences), Boling Guo (Beijing Institute of Applied Physics and Computational Mathematics) and Guoli Zhou (Chongqing University).

报告题目：Matching upper and lower moment bounds for a large class of stochastic PDEs driven by general

space-time Gaussian noises

报告人：胡耀忠 (University of Alberta)

报告时间：6月28日 10:00

报告地点：管理楼1418

报告摘要：In this talk, I will present a joint work with Xiong Wang about the matching upper and lower moment bounds for the solution of stochastic partial differential equations driven by a general Gaussian noises, which gives a complete answer to the open problem of the matching lower moment bounds for the stochastic wave equations for general Gaussian noises. In order to to assure this intermittency property we introduce two new general conditions for the Green's function of the equation: small ball nondegeneracy and bounded Hardy-Littlewood-Sobolev total mass, which are satisfied by a large class of stochastic PDEs, including stochastic heat equations, stochastic wave equations, stochastic heat equations with fractional Laplacians, and stochastic partial differential equations with fractional derivatives both in time and in space. The main technique to obtain the lower moment bounds is to develop a Feynman diagram formula for the moments of the solution, to find the manageable main terms, and to carefully analyse these terms of sophisticated multiple integrals by exploring the above two properties.

报告题目：Log-concavity of invariants from Legendrian knot theory and character varieties

报告人：苏桃（北京雁栖湖应用数学研究院）

报告时间：2024年6月28日 10：00-11：00

报告地点：2教2103

报告摘要：Basing on examples, we propose a conjecture on the log-concavity of ruling polynomials (Legendrian analogue of Jones polynomials) for Legendrian links. In the case of Legendrian torus knots, we prove the conjecture via a connection to the HOMFLY-PT polynomials. Moreover, we explain some algebraic geometry behind via some 'BPS calculus', in the case of Legendrian links arising from plane algebraic curve singularities. Finally, there is a natural generalization of the conjecture to character varieties. Based on work in progress.

物理学院

马克思主义学院

“旧物换新友”二手集市

活动时间：6月30日，16：00~19：30

活动地点：中国科学技术大学中区宿舍楼楼下

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