Spectral Geometry Seminar @ USTC
Schedule of 2023：Upcoming Talks
Speaker: Zhifeng WEI （Indiana University）
 Time：
 TBA
 Place：
 腾讯会议 TBA
 Title：
 Spectral Embedding, Signless Laplacian, and Random Walk Convergence
 Abstract：

For a simple random walk on a cycle graph with an odd number of vertices, the ergodic theorems of Markov chains tell us that the return probabilities satisfy $$\lim_{t\to\infty}p_t(x,x)=\tfrac{1}{n},$$
where $n$ is the number of vertices of the cycle and $p_t(x,x)$ is the probability that a simple random walk, started at a vertex $x$ of the cycle, returns to $x$ on step $t\geqslant 1$.
In this talk, we will consider general regular graphs and present a sharp bound on convergence rate: the return probabilities of a simple random walk on a regular nonbipartite graph $G$ (with $n$ vertices) satisfies
$$\abs[\big]{p_t(x,x)\tfrac{1}{n}}\leqslant \tfrac{18}{\sqrt{t}} $$
for $t\geqslant 1$ and each vertex $x$ of $G$.
Our main tool is the method of ``spectral embedding" based on the ``signless Laplacian" operator. Bounds on eigenvalues of random walk transition matrices will also be given as a byproduct.
Speaker: Fang WANG （Shanghai Jiaotong University）
 Time：
 TBA
 Place：
 TBA
 Title：
 TBA
 Abstract：
 TBA
Speaker: Xi CHEN （Shanghai Center for Mathematical Sciences）
 Time：
 TBA
 Place：
 TBA
 Title：
 TBA
 Abstract：
 TBA
Past Talks
Speaker: Jian WANG （The University of North Carolina at Chapel Hill）
 Time：
 July 5, 16:0017:00
 Place：
 2302
 Title：
 Damping for Fractional Wave Equations
 Abstract：
 Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give the explicit decay rates for the energy, but do not address reflection/transmission of waves at the interface of the damping. Still for a subset of the models considered, this represents the first result proving the decay of the energy of the surface wave models. Joint work with Thomas Alazard and Jeremy Marzuola.
Speaker: Hao XU （Zhejiang University）
 Time：
 June 15, 16:0017:00
 Place：
 5406
 Title：
 Spectral geometry of Kahler manifolds
 Abstract：
 First we survey known results on spectral geometry of Kahler manifolds. Then we study the question of the spectral characterization of CP^n. Namely for each fixed nonnegative integers p, if a compact Kahler manifold M of complex dimension n has the same pspectra as CP^n equipped with the FubiniStudy metric, we give explicit range of n such that this Kahler manifold is holomorphically isometric to CP^n . This extends previous works of Tanno, ChenVanhecke, Goldberg for p<=2 and Ping Li for even p. This is joint work with K. Liu, X. Huang and Y. Zhi.
Speaker: Xianchao WU (Wuhan University of Technology)
 Time：
 June 1, 16:0017:00
 Place：
 5406
 Title：
 Distribution of Schr\"{o}dinger eigenfunctions
 Abstract：

In this talk, we consider the distribution of eigenfunctions of the semiclassical Schr\"{o}dinger operator on a compact manifold. Their behaviors in forbidden regions and classically allowed regions are dramatically different.
In forbidden regions, we will introduce a partial converse to the Agmon estimates (ie. exponential lower bounds for the eigenfunctions) in terms of Agmon distance under a control assumption. Then by considering a Dirichlet problem with applying Poisson representation and exterior mass estimates on hypersurfaces, we will show a sharp reverse Agmon estimate on a hypersurface in the analytic setting.
However, in classically allowed regions, the behavior of Schr\"{o}dinger eigenfunctions is much more complicated. Intuitively, the more time a packet spends near a hypersurface the more concentration we would expect to see there. How to describe it quantitively? We show that if the defect measure $\mu$ associated to a sequence of Schr\"{o}dinger eigenfunctions is $\epsilon_0$ tangentially diffuse with respect to the hypersurface, then one can get $o(1)$ improvement of the well known $O(h^{1/4})$ restriction bounds.
Speaker: Yongqiang ZHAO (West Lake University)
 Time：
 May 25, 16:0017:00
 Place：
 5406
 Title：
 Eigenvalue mutiplicities and vanishing sums of roots of unity
 Abstract：

It is well known that the standard flat torus T^2=R^2/Z^2 has arbitrary large Laplacianeigenvalue multiplicies. Consider the discrete torus C_N * C_N with the discrete Laplacian operator; we prove, however, its eigenvalue multiplicities are uniformly bounded for any N, except for the eigenvalue one when N is even. Our main tool to prove this result is the beautiful theory of vanishing sums of roots of unity. In this talk, we will give a brief introduction to this theory and outline a proof of the uniformly boundedness multiplicity result.
Speaker: Cheng ZHANG (Tsinghua University)
 Time：
 April 28, 16:0017:00
 Place：
 5505
 Title：
 Sharp Lp estimates and size of nodal sets of generalized Steklov eigenfunctions
 Abstract：

We prove sharp Lp estimates for the Steklov eigenfunctions on compact manifolds
with boundary in terms of their L2 norms on the boundary. We prove it by establishing Lp
bounds for the harmonic extension operators as well as the spectral projection operators on the
boundary. Moreover, we derive lower bounds on the size of nodal sets for a variation of the
Steklov spectral problem. We consider a generalized version of the Steklov problem by adding a
nonsmooth potential on the boundary but some of our results are new even without potential.
Speaker: Yakun XI (Zhejiang University)
 Time：
 April 27, 16:0017:00
 Place：
 5205
 Title：
 Can you hear your location on a manifold?
 Abstract：

We introduce a variation on Kac's question, "Can one hear the shape of a drum?" Instead of trying to identify a compact manifold and its metric via its LaplaceBeltrami spectrum, we ask if it is possible to uniquely identify a point x on the manifold, up to symmetry, from its pointwise Weyl counting function. This problem has a physical interpretation. You are placed at an arbitrary location in a familiar room with your eyes closed. Can you identify your location in the room by clapping your hands once and listening to the resulting echos and reverberations?
Our main result provides an affirmative answer to this question for a generic class of metrics.
Speaker: Dong ZHANG (Peking University)
 Time：
 April 26, 16:3017:30
 Place：
 5307
 Title：
 Spectral duality as a tool for studying the nonlinear graph eigenvalue problems
 Abstract：

Nonlinear eigenvalue problems for pairs of homogeneous convex functions are particular nonlinear constrained optimization problems that arise in a variety of settings, including graph mining and network science. In this talk, I will show that one can move from the primal to the dual nonlinear eigenvalue formulation maintaining the spectrum, the variational spectrum as well as the corresponding multiplicities unchanged. Applications to the spectral theory of graph pLaplacians and Cheeger inequalities on simplicial complexes, will be discussed.
Speaker: Hongyi CAO (Peking University)
 Time：
 April 06, 14:3015:30
 Place：
 5407
 Title：
 Localization for quasiperiodic Schr\"odinger operators on $\mathbb{Z}^d$ with $C^2$cosine Like Potentials
 Abstract：

Anderson Localization (pure point spectrum with exponentially decaying eigenfunctions) is an important phenomenon in spectrum theory for quasiperiodic (QP) operators. In this talk, we will discuss lattice QP Schr\"odinger operators on $\mathbb{Z}^d (d\geq1)$ with $C^2$cosine like potentials. We will show quantitative Green's function estimates and the arithmetic version of Anderson localization for such QP Schr\"odinger operators. This talk is based on a joint work with my advisors Zhifei Zhang (Peking University) and Yunfeng Shi (Sichuan University).
Speaker: Zhenhao LI (University bielefeld )
 Time：
 March 31, 16:0017:00
 Place：
 5106
 Title：
 On synthetic Ricci curvature bounds on metricmeasure spaces
 Abstract：

Abstract: The setting of metricmeasure spaces with synthetic Ricci bounds (e.g. CD/RCD spaces) has attracted not only analysts but also quite many geometers. In this talk, I will first present the classical LottVillaniSturm theory on the synthetic lower Ricci bound relying on the convexity of entropy functionals. Also I will mention another description by the contraction of Wasserstein distances between heat flows, in the spirit of BakryEmery. If time permits, I will talk about recent topics on generalising above two viewpoints to the theory of Ricci flows.
Speaker: Guoyi XU (Tsinghua University)
 Time：
 March 20, 10:0011:00
 Place：
 5307
 Title：
 The first Dirichlet eigenvalue and the width
 Abstract：

There are a lot of result about the sharp lower bound of the first Dirichlet eigenvalue or Neumann eigenvalue under different restriction (back to FaberKrahn and PayneWeinberger for Euclidean domain, LiYau and ZhongYang for manifolds case). Generally, the sharp lower bounds of those eigenvalues are achieved on disk (sphere, for the case that boundary is empty, corresponding noncollapsed case) or line segment (circle, corresponding collapsed case). Recent years, there are research to characterize the difference between the domain and the model space (mentioned above), by the gap between the eigenvalue and its sharp bound (quantitative FaberKrahn inequality etc). And the results along this direction obtained so far, in the spirit, are close to the quantitative isoperimetric inequality established during the last decade (FuscoMaggiPratelli etc). The common point is that the model space is “homogenous in any direction (disk or sphere etc) and is noncollapsed.
In this talk, we present our recent result, which gives the explicitly quantitative inequality, linking the width of the domain with the gap between the first Dirichlet eigenvalue and its sharp lower bound. One novel thing is that our model space is collapsed line segment. Most part of this talk only requires the basic PDE and Riemannian geometry knowledge.
Schedule of 2022：Past Talks
Speaker: Olaf Post (University of Trier)
 Time：
 Dec 21, 16:0017:00
 Place：
 ZOOM：976 2601 7096 会议密码：137769
 Title：
 Some recent results on graph perturbations and the effect on their spectrum
 Abstract：

In this talk I will talk about joint works with Fernandó Lledo (Madrid) and John Fabila (Edinburgh) on the spectrum of discrete Laplacians on weighted magnetic graphs and its behaviour under perturbations such as removing edges, contracting vertices etc. One application is an easy spectral criterion whether a graph is Hamiltonian or not. Another application is a construction of families of isospectral graphs.
Speaker: Xiaolong Hans HAN (Yau Mathematics Science Center, Tsinghua University)
 Time：
 Dec 14, 10:0011:00
 Place：
 腾讯会议：588250072 会议密码：202223
 Title：
 Large Steklov eigenvalue on random hyperbolic surfaces
 Abstract：

We construct a sequence of hyperbolic surfaces with connected geodesic boundary such that the first normalized Steklov eigenvalue tends to inﬁnity, using the connection between eigenvalues and Cheeger's / Jammes's constants, and the recent work of Xin Nie, Yunhui Wu, and Yuhao Xue. Using the WeilPetersson metric, we also show that the probability that a random Riemann surface has a large 1st normalized Steklov eigenvalue is asymptotically one.
Speaker: Jing MAO （Hubei University）
 Time：
 Dec 07, 16:0017:00
 Place：
 腾讯会议：249108389 会议密码：202222
 Title：
 Polyatype inequalities on spheres and hemispheres
 Abstract：
 Given an eigenvalue $\lambda$ of the LaplaceBeltrami operator on nspheres and hemispheres, we characterise those with the lowest and highest orders which equal $\lambda$ and for which Polya's conjecture holds and fails. We further derive Polyatype inequalities by adding a correction term providing sharp lower and upper bounds for all eigenvalues. This allows us to measure the deviation from the leading term in the Weyl asymptotics for eigenvalues on spheres and hemispheres. As a direct consequence, we obtain similar results for domains which tile hemispheres. This talk is based on a jointwork with Prof. Pedro Freitas AND Prof. Isabel Salavessa.
Speaker: Changwei XIONG (Sichuan University)
 Time：
 October 26, 10:0011:00
 Place：
 腾讯会议：693367593 会议密码：202221
 Title：
 Some estimates on an exterior Steklov eigenvalue problem
 Abstract：
 In this talk we will discuss a Steklov eigenvalue problem on an exterior Euclidean domain. We will present sharp lower and upper bounds for its first eigenvalue under various conditions on the domain. Time permitting, we shall discuss an upper bound for its second eigenvalue.
Speaker: Yong LIN（Tsinghua University）
 Time：
 October 12, 10:0011:00
 Place：
 腾讯会议：449488884 会议密码：202220
 Title：
 Normalized discrete Ricci flow and community detection
 Abstract：
 我们证明了由图上离散的Ricci曲率定义的曲率流方程解的存在唯一性。同时我们利用这种曲率流方程研究图分割问题，并且比较了我们的图分割方法和其他经典的图分割方法。
Speaker: Longzhi LIN （UC Santa Cruz）
 Time：
 September 28, 10:3011:30
 Place：
 腾讯会议：419604062 会议密码：202219
 Title：
 Energy convexity and uniqueness of conformalharmonic maps
 Abstract：
 In this talk we will survey some recent results on the energy convexity for weakly harmonic and biharmonic maps and the applications. We will then introduce a conformally invariant analogue of the intrinsic biharmonic map that we call conformalharmonic map, which is a critical point of a conformally invariant energy functional in four dimension and satisfies a conformally invariant fourth order Paneitztype PDE. A version of energy convexity and uniqueness of conformalharmonic maps that we showed in a most recent joint work with J. Zhu will be discussed.
Speaker: Bobo HUA（Fudan University）
 Time：
 September 14, 16:0017:00
 Place：
1418
 Title：
 Some results of semilinear PDEs on lattice graphs
 Abstract：
 Yamabe type semilinear PDEs have been well studied on R^n. In this talk, we discuss some recent results on the lattice graph Z^n. Open questions are more than what we know. This is based on joint work with Ruowei Li and Florentin Muench.
Speaker: Asma HASSANNEZHAD（University of Bristol）
 Time：
 June 8, 16:0017:00
 Place：
 ZOOM ID: 945 8387 4680 Passcode: 695038
 Title：
 Nodal counts for the DirichlettoNeumann operators with potential
 Abstract：
 The zero set of an eigenfunction is called the nodal set and the connected components of its complement are called the Nodal domains. The wellknown Courant nodal domain theorem gives an upper bound for the nodal count of Laplace eigenfunctions on a compact manifold. We consider the harmonic extension of eigenfunctions of the DirichlettoNeumann operators with potential. When the potential is zero, these harmonic extensions are called the Steklov eigenfunctions. It has been known that the Courant nodal domain theorem holds for Steklov eigenfunctions. We discuss how we can get a Couranttype bound for the nodal count of the DirichlettoNeumann operator in the presence of a potential. This is joint work with David Sher.
Speaker: Lingzhong ZENG （Jiangxi Normal University）
 Time：
 June 1, 16:0017:00
 Place：
 腾讯会议：184674728 会议密码：202216
 Title：
 Universal Inequalities of Laplacian on Riemannian Manifolds and Extensions
 Abstract：
 In this talk, we would like to review some universal inequalities of Laplacian on Riemannian Manifolds. Furthermore, we consider the eigenvalues of Laplacian on the closed Riemannian manifolds. As an application, we give a very sharp upper bound for the second eigenvalue of Laplacian on the isoparametric hypersurface embeded in the unit sphere. Finally, we also give some universal bounds of Xin Laplacian on the translators in the sense of MCF. This is a work joint with Zhouyuan Zeng.
Speaker: Francesco TUDISCO (Gran Sasso Science Institute, L'Aquilla, Italy)
 Time：
 May 25, 16:0017:00
 Place：
 ZOOM ID: 942 6323 4612 Passcode: 713982
 Title：
 Nodal domain count of the generalized pLaplacian on graphs
 Abstract：
 We consider a generalized pLaplacian operator on discrete graphs which generalizes the linear Schrödinger operator (obtained for p=2).
We consider a set of variational eigenvalues of this operator and present new results that characterize several spectral properties of this operator with particular attention to the nodal domain count of its eigenfunctions. Just like the onedimensional continuous pLaplacian, we prove that the variational spectrum of the discrete generalized pLaplacian on forests is the entire spectrum. Moreover, we show how to transfer the Weyl’s inequalities for the Laplacian operator to the nonlinear case and thus we prove new upper and lower bounds on the number of nodal domains of every eigenfunction of the generalized pLaplacian on graphs, including those corresponding to variational eigenvalues. When applied to the linear case p=2, the new results imply wellknown properties of the linear Schrödinger operator as well as novel ones.
Speaker: Yuhua SUN (Nankai University)
 Time：
 May 18, 10:0011:00
 Place：
 腾讯会议：229902342 会议密码：202214
 Title：
 Some progress on semilinear elliptic inequalities involving gradient terms on weighted graphs
 Abstract：
 We study existence and nonexistence of nontrivial positive solutions to the following semilinear elliptic inequalities involving gradient terms on weighted graphs
$$\Delta u+u^p\nabla u^q\leq 0,$$
Where $(p, q)\in \mathbb{R}^2$.
This talk is based on joint works with Qingsong Gu, Lu Hao, Xueping Huang.
Speaker: Xi CHEN （Shanghai Center for Mathematical Sciences）
 Time：
 May 11, 10:0011:00
 Place：
 腾讯会议：120414316 会议密码：202213
 Title：
 锥流形上波的衍射现象
 Abstract：
 在具有锥奇性的黎曼流形上，波传播到锥点时会发生衍射现象，即波的传播分离成几何波和衍射波。我们用拟微分算子和傅里叶积分算子完整地刻画波的衍射现象。
Speaker: Genqian LIU (Beijing Institute of Technology)
 Time：
 April 27, 16:0017:00
 Place：
 腾讯会议：757475957 会议密码：202212
 Title：
 Heat trace asymptotic expansions for Lame elastic operator and the Stokes flow operator
 Abstract：
 Spectral asymptotics for partial differential operators have been the subject of extensive research for over a century. It has attracted the attention of many mathematicians and physicists. In this talk, we will give a survey about the spectral geometric problem for some famous differential operators. We then will discuss the heat trace asymptotic expansions for the Lame elastic operator and Stokes flow operator.
Speaker: Bobo HUA (Fudan University)
 Time：
 April 20, 10:0011:00
 Place：
 腾讯会议：182624802 会议密码：202211
 Title：
 Steklov eigenvalues on graphs
 Abstract：
 In this talk, we introduce the Steklov eigenvalue problems on graphs, and estimate the eigenvalues using geometric quantities.
Speaker: Yaoping HOU (Hunan Normal University)
 Time：
 April 13, 10:0011:00
 Place：
 腾讯会议：807608186 会议密码：202210
 Title：
 On spectra of signed graphs
 Abstract：
 In this talk, we I will introduce some recent results on eigenvalues of signed graphs, such as
signed graphs with few disitinct eigenvalues, integral subcubic signed graphs, the muliplicity of eigenvalues, and the signed graphs with spectral radius does not exceed $\sqrt{2+\sqrt{5}}.$
Speaker: Guoyi XU（Tsinghua University）
 Time：
 April 6, 10:0011:00
 Place：
 腾讯会议：981472543 密码：202204
 Title：
 The sharp estimates of functions and the related rigidity, stability
 Abstract：
 Since ChengYau proved the gradient estimate of harmonic functions in 1975, their method played important role in geometric analysis. Its philosophy was generalized to prove the lower bound of eigenvalues and parabolic Harnack estimate by LiYau. In this talk, we will discuss the sharp gradient estimate for harmonic functions, sharp Dirichlet eigenvalues in geodesic ball. Furthermore, we present the corresponding sharp estimate for Green's function and heat kernel, and the rigidity and stability of those estimates will also be discussed. This is a survey report based on my former work and the joint work with Haibin WangJie Zhou, and Qixuan HuChengjie Yu. Only basic Riemannian geometry and PDE knowledge is enough to understand most part of the talk.
Speaker: Xiaodong ZHANG (Shanghai Jiaotong University)
 Time：
 March 30, 10:0011:00
 Place：
 腾讯会议：910896042 密码：202203
 Title：
 The Discrete FaberKrahh Inequality of Graphs
 Abstract：
 The FaberKrahn inequality
states in spectral geometric theory that the ball has smallest first Dirichlet eigenvalue
among all bounded domains with the fixed volume in
$\mathbb{R}^n$. In this talk, the Dirichlet eigenvalues of graphs with boundary condition were introduced. Then some similar FaberKrahn inequalities were proved to be held for some classes of graphs, for example the set of all trees and connected unicyclic (bicyclic) graphs with a given graphic unicyclic (bicyclic) degree sequence $\pi$ under minor conditions.
Moreover, the extremal unicyclic (bicyclic) graph is unique and possess
spiral like ordering and can be regarded as ball approximations.
This talk is joined with GuangJun Zhang (张光军, 青岛科技大学), Jie Zhang (张杰， 上海立信会计金融学院)
Speaker: Chengjie YU (Shantou University)
 Time：
 March 23, 16:0017:00
 Place：
 腾讯会议：530921280 密码 202203
 Title：
 Minimal Steklov Eigenvalues on Combinatorial Graphs
 Abstract：
 In this talk, we will present some details of our recent work on extending Jeol Friedman's theory on nodal domains for Laplacian eigenfunctions on combinatorial graphs to Steklov eigenfunctions and applying it to solve an minimum problem on Steklov eigenvalues for combinatorial graphs which is also an extension of Friedman's theory on solving a similar minimum problem on Laplacian eigenvalues. This talk is based on a joint work with Yingtao Yu.
Speaker: Linlin SUN (Wuhan University)
 Time：
 March 16, 16:0017:00
 Place：
 腾讯会议 101578059 Passcode 202203
 Title：
 Rigidity results of CSL submanifolds in the unit sphere
 Abstract：
 I will talk about the rigidity of contact stationary Legendrian (CSL) submanifolds in the unit sphere based on the joint works with Prof. Luo Yong and Dr. Yin Jiabin. We prove some optimal rigidity results of closed CSL submanifolds and obtain a new characterization of the minimal Calabi torus in the unit sphere.
Speaker: Shicheng XU (Capital Normal University)
 Time：
 March 09, 10:0011:00
 Place：
 腾讯会议 126609398 密码 202203
 Title：
 Total squared mean curvature of immersed submanifolds in a negatively curved space
 Abstract：
 Let n≥2 and k≥1 be two integers. Let M be an isometrically immersed closed submanifold of dimension n and codimension k, which is homotopic to a point, in a complete manifold N, where the sectional curvature of N is no more than δ<0. We prove that the total squared mean curvature of M in N and the first nonzero eigenvalue λ_1(M) satisfies
λ_1(M)≤ n(δ +Vol^(1)(M) ∫ H^2 dvol.
The equality implies that M is minimally immersed in a geodesic sphere after lifted to the universal cover of N. This completely settles an open problem raised by E. Heintze in 1988.
Speaker: Dong ZHANG （MaxPlanck Institute for Mathematics in the Sciences, Leipzig）
 Time：
 March 02, 16:0017:00
 Place：
 腾讯会议：385544473 Passcode: 202202
 Title：
 Some progresses on spectra of discrete structures
 Abstract：
 Simplicial complexes, graphs and hypergraphs are typical discrete structures that can be studied by employing methods in spectral theory. In this talk, I will present some recent developments on spectra of discrete structures. This includes new results on maximal gap intervals for the graph Laplacian; a refined analysis of the variational and nonvariational eigenvalues of the graph pLaplacian; the nonlinear spectral duality for convex and homogeneous function pairs, and its applications to hypergraph pLaplacians, and Cheeger inequalities on simplicial complexes.
Speaker: Norbert PEYERIMHOFF（Durham University）
 Time：
 February 25, 16:0017:00 (Beijing Time)
 Place：
 （UPDATED） Zoom: 98661278861 Passcode: 980641
 Title：
 Some applications of an improved Cheeger inequality by Kwok et al
 Abstract：
 In 2013, Kwok, Lau, Lee, Oveis Gharan and Trevisan gave an improved Cheeger inequality in the graph theoretical setting. This inequality involves, besides the first positive eigenvalue and the Cheeger constant, also higher Laplace eigenvalues.
In this talk, I will discuss this improved Cheeger inequality and present some applications of its counterpart in the smooth setting of Riemannian manifolds. The talk will cover results by Shiping Liu and also results derived in collaboration with him and Matthias
Keller.
Speaker: Zhiqin LU（UC Irvine）
 Time：
 January 21, 10:0011:00 (Beijing Time)
 Place：
 腾讯会议：772909850 Passcode: 202201
 Title：
 On manifold with positive spectrum
 Abstract：
 In this talk, I will first present my joint work with Bobo Hua on manifold with positive spectrum with respect to a Schrodinger operator. On a relevant topic, I will then present the discontinuity phenomena of eigenfunctions on singular space and its applications in constructing manifold with essential spectrum gaps.
Speaker: Juergen JOST（MaxPlanck Institute for Mathematics in the Sciences, Leipzig）
 Time：
 January 14, 16:0017:00 (Beijing Time)
 Place：
 Zoom：91088937796 Passcode: 545110
 Title：
 Spectra of graphs and hypergraphs
 Abstract：
 In this talk, after recalling results about the spectrum of the normalized Laplacian of a graph, I shall introduce a Laplace operator for a class of hypergraphs that model chemical reaction systems, and I shall present the corresponding spectral theory. This will include Cheeger type inequalities.
The talk will represent joint work with Raffaella Mulas and Zhang Dong.