全部视频在校内视频网站：wlkt.ustc.edu.cn
视频网站链接(个人录制，清晰度和质量没有前者高)：
https://space.bilibili.com/239916542/video
腾讯会议：427-630-7535
https://meeting.tencent.com/p/4276307535
密码：464569
Zoom：
https://us06web.zoom.us/j/8784574760
密码：111111
研究生教育创新计划高水平学术前沿系列报告
主题：拓扑递归
报告人：周坚，清华大学
时间与地点：2024年11月28日周四14:30-17:00，5401; 11月30日周六9:30-12:00，5102
题目:拓扑递归介绍
摘要: 我们将介绍拓扑递归的来源和与代数曲线的模空间上相交数的关系。我们将集中在谱曲线仅有一个分岔点的情形。
报告人：宗正宇，清华大学
时间与地点：2024年11月30日周六14:00-16:30，5102; 12月1日周日9:30-12:00，5102
题目: Topological recursion and enumerative geometry
摘要: In this series of courses, I will first introduce the definition and basic properties of topological recursion. Then I will talk about the relation
between topological recursion and enumerative geometry. I will give serveral examples including the Witten-Kontsevich tau function, the Weil-Petersson Volume,
Hurwitz numbers, the Gromov-Witten theory of the projective line, and the Gromov-Witten theory of toric Calabi-Yau 3-folds/3-orbifolds. If time permits,
I will talk about more examples and the relation to semi-simple cohomological field theories.
题目: Quantum trace maps for SL(n)-skein algebras
报告人：俞韬，南方科技大学
时间：2024年11月6日（星期三）10：00
地点：东区五教5407教室
摘要：The skein algebra of a surface is a quantization of the character variety, and the quantum trace map is a quantization of the classical trace map that sends a curve on the surface to the coordinate expression of the trace function. We review the n=2 case constructed by Bonahon-Wong and describe the generalization to all n.
题目: Shape of Thurston's filling systole subset in surface moduli space
报告人：高悦，安徽师范大学
时间：2024年9月9日（星期一）14：00
地点：东区五教5102教室
摘要：In this talk, I am going to talk about the sparseness of Thurston's subset. Sparseness is a geometric concept on Thurston's subset first raised by Anderson- Parlier-Pettet in 2016. We have proved the sparseness of Thurston's subset in the sense of Teichmüller distance and Weil-Petersson distance. More precisely, most surfaces in genus g surface moduli space have Teichmüller distance $\frac{1}{5}\log\log g$ and Weil- Petersson distance $0.6521(\sqrt{\log g} − \sqrt{7\log\log g})$ to the Thurston's subset.
题目: Thurston volume of the unit balls associated to holomorphic quadratic differentials
报告人：苏伟旭，中山大学
时间：2024年9月5日（星期四）16：00
地点：东区五教5104教室
摘要：Let q be a holomorphic quadratic differential on a compact Riemann surface. We can associate q with a flat metric and a unit ball of the measured lamination space. We study the Thurston volume of the unit ball and give lower and upper bounds for the volume function on the moduli space. This is a joint work with Shenxing Zhang.
题目：Hassett-Keel program and moduli spaces of Abelian differentials
报告人：于飞（浙江大学）
时间：6月26日9：00
腾讯会议：600-3929-5239
https://meeting.tencent.com/dm/Ji5zXJqWY1VB
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.
题目: Picard群上的大筛法不等式
报告人：齐治，浙江大学
时间：2024年6月18日14：00
地点: 东区第五教学楼104教室
摘要: 在报告中我们会讨论如何建立Picard群PGL(2, Z[i])上的大筛法不等式与有特殊特征扭的大筛法不等式。
题目: Introduction to Rankin-Selberg theory on GL(n)
报告人：柴劲松，安徽工程大学
时间地点:
2024年6月17日9：45 东区第五教学楼207教室
2024年6月18日 9：45 东区第五教学楼104教室
2024年6月19日 14：00 东区第二教学楼204教室
摘要: These are three lectures on Rankin-Selberg theory on GL(n). In lecture one, we will recall certain representation theory background needed. Lecture two will focus on basic results of Rankin-Selberg on GL(n), both locally and globally. In lecture three, we will discuss some applications of the theory to Langlands Functoriality problem.
题目: The asymptotic plateau problem, a brief history and recent progress
报告人：Zheng Huang，City University of New York
时间: 2024年6月11日，10：00
地点：东区第五教学楼106教室
摘要: Given a closed Jordan curve on the sphere at infinity, the asymptotic plateau problem asks the existence (and other related) questions of minimal surfaces in H^3 spanned by the curve. In this talk, I will review some old theorems and discuss a few new results.
题目：Pullback of symplectic forms to the space of circle patterns
报告人：林伟扬（卢森堡大学）
时间：5月14日15：00
腾讯会议：600-3929-5239https://meeting.tencent.com/dm/Ji5zXJqWY1VB
摘要：We consider circle patterns on surfaces with complex projective structures. We investigate two symplectic forms pulled back to the deformation space of circle patterns. The first one is Goldman's symplectic form on the space of complex projective structures on closed surfaces. The other is the Weil-Petersson symplectic form on the Teichmüller space of punctured surfaces. We show that their pullbacks to the space of circle patterns coincide. It is applied to prove the smoothness of the deformation space, which is an essential step to the conjecture that the space of circle patterns is homeomorphic to the Teichmüller space of the closed surface.
系列报告人：徐晓濛，北京大学国际数学研究中心
时间: 2024年5月10日，9：45
地点：东区第五教学楼407教室
题目: An introduction to the Stokes phenomenon and isomonodromy deformation
摘要: This talk gives an introduction to the Stokes matrices of a linear meromorphic system, and the associated nonlinear isomonodromy deformation equation. In the case of Poncare rank 1, the nonlinear equation naturally arises from the theory of Frobenius manifolds, stability conditions, Poisson geometry, representation theory and so on, and can be seen as a higher rank generalizations of the sixth Painlevé equation.
时间: 2024年5月10日，14：00
地点：东区第五教学楼206教室
题目: Solving the isomonodromy equation via the Riemann-Hilbert method
摘要: This talk solves the isomonodromy equation, in the sense that it gives a parameterization of the asymptotics of the solutions of the isomonodromy equation at a critical point, the explicit formula of the monodromy/Stokes matrices of the linear problem, as well as a connection formula between two differential critical points. As an application, the regularized limits of Stokes matrices are given. It is partially based on a joint work with Qian Tang.
题目: The WKB approximation in the Stokes phenomenon and Cauchy interlacing inequality
摘要: This talk studies the WKB approximation of the linear meromorphic systems of Poncaré rank 1, via the isomonodromy approach. It unveils a relation between the WKB approximation of the Stokes matrices, the Cauchy interlacing inequality and cluster algebras. It is based on a joint work with Anton Alekseev, Andrew Neitzke and Yan Zhou.
时间: 2024年5月11日，8：30
地点：东区第五教学楼502教室
题目: Quantum Stokes phenomenon and quantum irregular Riemann-Hilbert map
摘要: This talk introduces the universal quantum linear ordinary differential equations at an arbitrary order pole. It then proves that the quantum Stokes matrices, of the differential equation at a k-th order pole, give rise to an associative algebra, that quantize the Poisson structure on the moduli space of meromorphic connections at a k-th order pole. In the case k=2, the associative algebra involved is the Drinfeld-Jimbo quantum group. Our results give a dictionary between the Stokes phenomenon at 2nd order pole and the representation theory of quantum groups, including at the roots of unit, the Gelfand-Testlin, crystal basis and so on.
题目: Complex Earthquakes and the Deligne-Mumford compactification of the moduli space
报告人：胡光明，南京邮电大学
地点：五教204
时间：2024年4月16日（周二），14：00
摘要: It is known that the Deligne-Mumford compactification $\overline{\mathcal{M}}^{DM}_{g,n}$ of the moduli space $\mathcal{M}_{g,n}$ is a projective algebraic variety. In this paper, we construct a new space $\overline{\mathcal{M}}^{ce}_{g,n}$, homeomorphic to $\overline{\mathcal{M}}^{DM}_{g,n}$, by the projections of complex earthquakes for one weighted simple closed curve in $\mathcal{M}_{g,n}$. Moreover, we give a formula of limit distance between complex earthquake and Teichm\"uller disk in moduli space.
题目: The Frobenius map and the Unicity theorem for stated sln-skein algebras
报告人：王志浩，新加坡南洋理工大学&格罗宁根大学
线上腾讯会议：600-3929-5239
https://meeting.tencent.com/dm/Ji5zXJqWY1VB
时间：2024年4月15日（周一），15：00
摘要: The stated sln-skein algebra is a quantization of the sln-representation variety. I will review the definition of this algebra, and it's classical limit. Bonahon-Wong constructed the the Frobenius map for the sl2-skein algebra, which was generalized to the stated sl2-skein algebra by Thang, Korinman, etc. The Frobenius map is important to study the center and the representation theory for the (stated) skein algebra. I will review sl2-Frobenius map, then talk about the construct of the sln-Frobenius map, and the unicity theorem for the stated sln-skein algebra.
题目：Generalized circle packings in hyperbolic background geometry and total geodesic curvatures
报告人：周朴淳，复旦大学
时间: 2023年4月15日（周一），9：00
地点：五教205
摘要: This report will introduce the problem of prescribed total geodesic curvatures of generalized circle packing in hyperbolic background geometry. For the circle packing, total geodesic curvatures is a new research object that was introduced by Xin Nie. I will introduce the generalization of it in the hyperbolic background geometry, and the existence and uniqueness of circle packings with prescribed total geodesic curvatures. My report is from the joint work of Guangming Hu, Yi Qi, and Yu Sun.
题目: On second eigenvalues of closed hyperbolic surfaces for large genus
报告人：吴云辉，清华大学
地点：东区第二教学楼103教室
时间：2024年3月29日（周五），14：00
摘要: In this work we obtain optimal lower and upper bounds for second eigenvalues of closed hyperbolic surfaces for large genus. Moreover, we also study their asymptotic behaviors on random hyperbolic surfaces. This is a joint work with Yuxin He.
题目：Counting Graphs on Surfaces
报告人：Jayadev Athreya，University of Washington
时间: 2023年1月26日（周五），23：00
Zoom：
https://us06web.zoom.us/j/8784574760
密码：111111
摘要: We describe two problems regarding counting graphs on surfaces, which generalize the idea of counting closed geodesics on surfaces. The first part of the talk, concerning theta-graphs on flat tori, is joint work with Aulicino and Richman, and the second, concerning triangulations on hyperbolic surfaces, is joint with Aougab.
题目：The valuation pairing on an upper cluster algebra
报告人：Bernhard KELLER，Université Paris Cité（巴黎西岱大学，原巴黎大学）
时间: 2023年12月29日（周五），下午14：30
地点：东区第五教学楼107教室
摘要: This talk is based on the joint work with Peigen Cao and Fan Qin. After a reminder on cluster algebras (K2 and Poisson), we will define the valuation pairing on an upper cluster algebra and present its basic properties. The main part of the talk will be devoted to several applications conerning d-vectors, exchange pairs, factoriality and F-polynomials.
时间: 2023年12月4日, 下午14：00
地点：5505
报告人：何东泰， 同济大学
题目：hyperbolic ribbon fibered knots with right-veering monodromies
摘要：We construct a family of hyperbolic ribbon fibered knots with rightveering monodromies, contrary to low-crossing examples and Floer-homologically thin knots. In particular, we expand the construction of Kazez and Roberts to produce hyperbolic fibered knots with various fractional Dehn twist coefficients. We also compare this result to the relationship between 3-genus and fibered knots in S3.
时间: 2023年12月1日, 上午10：00
地点：5305
报告人：Andrei Moroianu, CNRS, Université Paris-Saclay
题目：On the ergodicity of the frame flow
摘要：The geodesic flow of compact Riemannian manifolds with negative sectional curvature is ergodic with respect to the Liouville measure on the unit tangent bundle. Its natural lift to the orthonormal frame bundle, called the frame flow, is only partially hyperbolic, and is not always ergodic, e.g. when the manifold is Kähler. In the 80's, Brin and Gromov proved the ergodicity of the frame flow when the dimension $n$ of the manifold is odd and different from 7, and conjectured that ergodicity should hold whenever the sectional curvature is at least 0,25 pinched. Some partial results were obtained by Brin-Karcher ('84) and Burns-Pollicott ('03), under quite strong pinching assumptions of the order of 0,86 and 0,98. In this talk I will report on some recent developments towards the Brin-Gromov conjecture, where the required pinching is approximately 0,27 - 0,29 for $n=4k+2$ and 0,57 - 0,6 for $n=4k$. The talk is based on joint work with Mihajlo Cekic (ETH, Zürich), Thibault Lefeuvre (Sorbonne Université) and Uwe Semmelman (Stuttgart University).
时间: 2023年10月20日, 上午10：00-11：00
地点：5405
报告人：Christian Blanchet, Université Paris Cité
题目：Heisenberg homologies of surface configurations
摘要：Motivated by the Lawrence-Krammer-Bigelow representations of the classical braid groups, we study the homology of unordered configurations in an orientable genus-g surface with one boundary component, over non-commutative local systems defined from representations of the discrete Heisenberg group. We discuss the resulting representations of the mapping class groups. Joint work with Martin Palmer and Awais Shaukat, https://arxiv.org/abs/2109.00515
时间: 2023年8月8, 10, 11日, 上午10：00-12：00
地点：2103
报告人：戴嵩(天津大学)
题目：Introduction to Higgs bundles over Riemann surfaces
摘要：The concept of Higgs bundles over Riemann surfaces was first introduced by Nigel Hitchin in 1987. Later the non-Abelian Hodge theory was established by relating Higgs bundles to flat bundles and harmonic maps. In recent years, the moduli space of the Higgs bundles is extensively studied due to its rich structures.
In this course, our goal is to provide a brief introduction to the theory of Higgs bundles over Riemann surfaces. In the first part, we will introduce the non-Abelian Hodge theory. In the second part, we will discuss the moduli space of Higgs bundles. We will focus on the aspect of the differential geometry of Higgs bundles. Being familiar with vector bundles and connections will help understanding the story.
时间: 2023年7月5日、7月6日、7月12日、 7月13日, 上午9：30-11：30
地点：东区第二教学楼2402教室
报告人：翁达平，UC Davis
题目: Legendrian weaves and cluster algebra
摘要: Legendrian weaves were introduced by Casals and Zaslow in 2020 as a combinatorial description of certain Legendrian surfaces in the standard contact R^5. In many cases, the Lagrangian projection of these Legendrian surfaces gives exact Lagrangian fillings of Legendrian links. The Kashiwara-Schapira moduli space of such a Legendrian link carries a cluster structure, and the combinatorics of this cluster structure is again nicely captured by Legendrian weaves. Legendrian weaves provide a new symplectic perspective on many known cluster structures, including positroid strata in Grassmannian and double Bott-Samelson cells, and give us a new geometric understanding of Donaldson-Thomas transformations on cluster varieties. In this lecture series, we will discuss some basics of Legendrian weaves and cluster structures, and give many examples demonstrating the close connection between them. If time allows, we will also discuss the new construction of cluster structures on braid varieties by Casals, Gorsky, Gorsky, Le, Shen, and Simental.
时间，地点：
东区第五教学楼5402教室，2023年5月31日（周三） 10:00
东区第五教学楼5205教室，2023年5月31日（周三） 14:00
东区第五教学楼5402教室，2023年6月1日（周四） 10:00
报告人：覃帆, 上海交通大学
题目：Bracelets are theta functions
摘要：The skein algebra of a marked surface possesses the basis of bracelet elements constructed by Fock-Goncharov and Musiker-Schiffler-Williams. As a cluster algebra, it also admits the theta basis from the cluster scattering diagram by Gross-Hacking-Keel-Kontsevich.
In this series of talks, we show that the two bases coincide except for the once-punctured torus. It is based on a joint work with Travis Mandel. Our results extend to quantum cluster algebras with coefficients arising from the surface even in punctured cases. Long-standing conjectures on strong positivity and atomicity follow as corollaries. We also connect our results to Bridgeland's stability scattering diagrams.
时间：5月18号（周四）16:00
Zoom
报告人：戴娴，波鸿鲁尔大学
题目：Correlation of Length Spectrums for Hitchin representations
摘要：In this talk, we present a correlation theorem of length spectrums for Hitchin representations. It is motivated by the study of correlations between hyperbolic structures by Richard Schwartz and Richard Sharp using thermodynamic formalism. We give some examples of different behaviors of correlation numbers of representations when considering special diverging sequences in Hitchin components.
时间：4月27号（周四）14:00
Zoom
报告人：Tsukasa Ishibashi, Tohoku University
题目：Moduli space of decorated G-local systems and skein algebras
摘要: The moduli space of decorated (twisted) G-local systems on a marked surface, originally introduced by Fock–Goncharov, is known to have a natural cluster K_2 structure. In particular, it admits a quantization via the framework of quantum cluster algebras, due to Berenstein—Zelevinsky and Goncharov—Shen. In this talk, I will explain its (in general conjectural) relation to the skein algebras. This talk is based on joint works with Hironori Oya, Linhui Shen and Wataru Yuasa.
时间： 2023年4月7日（周五）16:30-17:30
Zoom
会议号：878 457 4760
报告人：Subhojoy Gupta, Indian Institute of Science
报告题目：Entropy, domination and quasi-Hitchin representations
摘要：A famous result of Bowen implies that the entropy or critical exponent of a strictly quasi-Fuchsian representation is strictly greater than that of a Fuchsian one. I will explain how this follows from domination results comparing marked length spectrums, and talk about a generalization of Bowen’s result in the context of surface-group representations into PSL(n,C) for n>2.
时间： 2023年3月2日（周四）16:30-17:30
Zoom
报告人：Tsouvalas Konstantinos, IHES
报告题目：Linear hyperbolic groups indiscrete in rank 1 and products
摘要：Gromov hyperbolic groups is a rich class of finitely presented groups introduced by Gromov in the 80s, capturing the coarse geometric properties of fundamental groups of closed negatively curved Riemannian manifolds. While there are certain classes of hyperbolic groups which can be realized as discrete subgroups of some general linear group over C (e.g. Anosov groups), there are no known linear examples which fail to admit discrete faithful complex representations. In this talk, we are going to provide constructions of linear hyperbolic groups which fail to admit discrete faithful representation into any semisimple Lie group of rank 1 or in products of rank 1 Lie groups. These are joint works independently with Sami Douba and Nicolas Tholozan.
视频
时间： 2023年2月24日（周五）16:30-17:30
报告人：黄鹏飞, Heidelberg University
报告题目：A nonabelian Hodge correspondence for filtered G-local systems
摘要：Local systems can be studied through the monodromies of algebraic vector bundles with regular integrable connections by the celebrated Riemann-Hilbert correspondence of Deligne. This equivalence was put by Simpson into his tame nonabelian Hodge correspondence through incorporating parabolic structures (i.e. weighted filtrations) at the divisors, resulting a correspondence between filtered local systems and parabolic Higgs bundles. However, when the structure group is generalized from GLn(C) to an arbitrary complex reductive G, due to some monodromy issues, it will be failed to achieve a satisfactory correspondence by considering parabolic structures merely. Finding the correct objects that correspond to filtered G-local systems is an interesting problem. In this talk, we will follow Boalch's idea of parahoric Bruhat-Tits's group scheme theory to provide a complete tame nonabelian Hodge correspondence that involves filtered G-local systems. If time permits, the wild correspondence will be mentioned as well. Based on recent joint work with G. Kydonakis, H. Sun and L. Zhao, and with H. Sun.
视频
时间： 2023年2月10日（周五）16:30-17:30
报告人：Andrés Sambarino, Institut de Mathématiques de Jussieu-Paris Rive Gauche
报告题目：Zariski closures of groups whose limit set contains a positive triple of flags
摘要：Hitchin representations are a class of representations of surface groups into simple split real Lie groups introduced by Hitchin in the 90's. They have attracted a lot of attention probably because of their remarkable resemblance between the (nowadays called) Hitchin component of \pi_1S with values in G, and the classical Teichmüller space of the surface S.
In this lecture we will discuss a new proof based on Lusztig's positivity of triples, of a result by Guichard on the classification of Zariski closures of Hitchin representations.
视频
时间： 2022年12月23日（周五）14:30-15:30
报告人：林伟扬, University of Luxembourg
报告题目：Deformation space of circle patterns
摘要：William Thurston proposed regarding the map induced from two circle packings with the same tangency pattern as a discrete holomorphic function. A discrete analogue of the Riemann mapping is deduced from Koebe-Andreev-Thurston theorem. One question is how to extend this theory to Riemann surfaces and relate classical conformal structures to discrete conformal structures. Since circles are preserved under complex projective transformations, we consider circle packings on surfaces with complex projective structures.
Kojima, Mizushima and Tan conjectured that for a given combinatorics the deformation space of circle packings is diffeomorphic to the Teichmueller space. In this talk, we explain how graph Laplacian is used and the extension to infinite circle patterns on open disks.
视频
演讲稿
时间： 2022年12月2日（周五）13:30-14:30
报告人：翁达平，UC Davis
报告题目：Grid plabic graphs, Legendrian weaves, and cluster structures
摘要： We construct a Legendrian link in R^3 from a “grid” plabic graph on R^2. We study a moduli space problem associated with the Legendrian link and construct a natural cluster structure on this moduli space using Legendrian weaves. In particular, we prove that any braid variety associated with (beta Delta) for a 3-strand braid beta admits cluster structures with an explicit construction of initial seeds. We also construct Donaldson-Thomas transformations for these moduli spaces. In this talk, I will introduce the theoretical background and describe the basic combinatorics for constructing Legendrian weaves and the cluster structures from a grid plabic graph. This is based on a joint work with Roger Casals (arXiv:2204.13244).
视频
时间： 2022年11月25日（周五）14:30-15:30
报告人：张影，苏州大学
报告题目：Trace polynomials for closed curves on the enlarged modular torus: Positivity and log-concavity
摘要： In joint work with Xiangfei Li, we study the associated trace polynomials for closed curves on the enlarged modular torus. For the coefficient sequences of the polynomials, we prove positivity for all curves, and log-concavity for all simple closed curves. We observe the same phenomina for enlarging all hyperbolic tori.
视频
演讲稿
时间： 2022年11月18日（周五）14:30-15:30
报告人：Tengren Zhang，National University of Singapore
报告题目：Entropy Rigidity for cusped Hitchin representations
摘要： Let G be a geometrically finite subgroup of PSL(2,R). We say that a representation r from G to PGL(d,R) is a Hitchin representation if there is an r-equivariant positive map from the real projective line to the space of complete flags in R^d. We then prove a rigidity result for the entropy of Hitchin representations, generalizing previous work of Potrie-Sambarino. This is joint work with Richard Canary and Andrew Zimmer.
视频
时间： 2022年11月10日（周四）10:00-11:00
报告人：杨文元，北京大学北京国际数学研究中心
报告题目：Conformal density for groups with contracting elements
摘要： In 1976, S. Patterson introduced a class of conformal measures on the limit set of Fuchsian groups, and further developed by D. Sullivan in Kleinian groups with various applications in spectral geometry, Mostow rigidity, geodesic flows and complex dynamics etc. These now called Patterson-Sullivan measures are important instances of conformal density for rank-1 symmetric spaces. In this talk, we will explain how to establish a theory of Patterson-Sullivan measures on the horofunction boundary for any discrete groups on geodesic metric spaces with contracting elements. Such group actions contain CAT(0) groups and mapping class groups, so our theory could be applied. Applications to growth problems and geodesic flows shall be mentioned, if time permits.
视频
演讲稿
时间： 2022年10月28日（周五）10:00-11:00
Zoom
报告人：沈临辉，Michigan State University
报告题目: Cluster Nature of Quantum Groups
摘要：By applying the cluster theory of higher Teichmuller spaces, we present a rigid cluster model to realize the quantum group $U_q(g)$ for $g$ of type ADE. That is, we prove that there is a natural Hopf algebra isomorphism from the quantum group to a quotient algebra of the Weyl group invariants of a Fock-Goncharov quantum cluster algebra. By applying the quantum duality of cluster algebras, we show that the quantum group admits a cluster canonical basis $\Theta$ whose structural coefficients are in $\mathbb{N}[q^{\frac{1}{2}}, q^{-\frac{1}{2}}]$. The basis $\Theta$ satisfies an invariance property under Lusztig's braid group action, the Dynkin automorphisms, and the star anti-involution.
视频
演讲稿
时间： 2022年10月21日（周五）15:30-16:30
报告人：谢羿，北京大学北京国际数学研究中心
报告题目：Knots, links, spatial graphs and their representation varieties
摘要：The fundamental groups can strongly reflect the geometric and topological properties of 3-manifolds. One approach to understand the fundamental groups is to study their representations into linear groups such as SU(2) or SO(3). In the past, the existence of non-abelian SU(2) representations has been proved for the fundamental groups of many different classes of 3-manifolds, including the complement of any non-trivial knot. Most of these results are obtained using techniques from gauge theory. More surprisingly, these techniques have been generalized by Kronheimer and Mrowka to the situation of spatial graphs (graphs embedded in the space). It is known that the four color theorem is equivalent to the existence of certain representations of planar cubic graphs (viewed as spatial graphs) into the Klein 4-group, which is a subgroup of SO(3). Therefore Kronheimer and Mrowka’s theory provides a potential way to obtain a computer-free proof of the four color theorem. In this talk, I will give an introduction to their theory and review various results on representations of the fundamental groups of the complements of knots, links and spatial graphs. Part of this talk is joint work with Boyu Zhang.
视频
演讲稿
时间： 2022年10月14日（周五）14:30-15:30
报告人：何思奇，中国科学院数学与系统科学研究院晨兴数学中心
报告题目: Kapustin-Witten equations and higher Teichmuller theory
摘要：We will discuss Witten's gauge theory approach to Jones polynomial by counting solutions to Kapustin-Witten equations with singular boundary conditions. We will discuss the relationship of these equations with the higher Teichmuller theory. This is joint work with R.Mazzeo.
视频
演讲稿
时间： 2022年10月7日（周五）14:30-15:30
报告人：戴嵩，天津大学应用数学中心
报告题目： Bounded differentials on unit disk and the associated geometry
摘要：Let D be the unit disk with hyperbolic metric. Given a holomorphic quadratic differential q, there is a harmonic map f from D to itself such that q is the Hopf differential. Under certain completeness condition, Wan showed that q is bounded (with respect to the hyperbolic metric) is equivalent to either the energy density is bounded or f is quasi-conformal. In this talk, we study more holomorphic differentials and the associated geometries. For holomorphic cubic, quartic and sextic differentials, the associated geometries are hyperbolic affine spheres in R^3, maximal surfaces in H^{2,n} and J-holomorphic curves in H^{4,2}. Combining Wan's PDE approach and Higgs bundle techniques, we show that under the completeness condition, the holomorphic differential is bounded is equivalent to either the induced metric is mutually bounded with the hyperbolic metric or the curvature of the induced metric is bounded above by a negative constant. We also generalize Wan’s result from the single equation to the equation system, which relates to the Toda system and the Hitchin equation in the non-Abelian Hodge theory. This is a joint work with Qiongling Li.
视频
演讲稿
时间： 2022年9月30日（周五）14:30-15:30
报告人：刘毅，北京大学北京国际数学研究中心
报告题目: Virtual homological eigenvalues and the Weil--Petersson translation length
摘要: For any pseudo-Anosov surface automorphism, I will discuss an inequality bounding certain growth of virtual homological eigenvalues with the Weil--Petersson translation length. The new inquality fits nicely with other known inequalities due to Kojima and McShane, and due to Le.
视频
时间： 2022年9月23日（周五）14:30-15:30
腾讯会议：647-4448-8711
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报告人：吴云辉，清华大学丘成桐数学科学中心
报告题目： Recent progress on first eigenvalues of hyperbolic surfaces for large genus
摘要：In this talk we wil discuss several recent results on first eigenvalues of closed hyperbolic surfaces for large genus. For example, we show that a random hyperbolic surface of large genus has first eigenvalue greater than $\frac{3}{16}-\epsilon$, extending Mirzakhani's lower bound $0.0024$. This talk is based on several joint works with Yuhao Xue.