Past semesters
Spring 2025, Fall 2024, Spring 2024, Fall 2023, Spring 2023, Fall 2022, Fall 2021- Spring 2022 (scroll down on linked page), Fall 2020 – Spring 2021, Fall 2019 – Spring 2020, Fall 2018 – Spring 2019,
[Admin note: Eventually, I intend to paste previous semesters’ schedules below. For now, please use the links above if the semester is missing from below.]
Schedule — Fall 2025
| Date | Speaker | Title |
|---|---|---|
| Sep 17 | Minghao Miao (Nanjing University / Rutgers New Brunswick) | The Volume of K-Semistable Fano Manifolds |
| Sep 24 | No colloquium | |
| Oct 1 | Alex He (Oklahoma) | Practical algorithms in 3-manifold topology |
| Oct 8 | Grace Garden (IMJ-PRG) | Character varieties and essential surfaces |
| Oct 15 | Yikai Teng (Rutgers Newark) | Khovanov homology and exotic planes |
| Oct 22 | No colloquium | |
| Oct 27* | Robert Bryant (Duke) | A visit to the Finsler world (*part of the Distinguished Lectures in Topology, Geometry, and Physics) |
| Oct 29 | Ao Sun (Lehigh) | Singular behavior of mean curvature flow |
| Oct 31 *(10:30am, Zoom only – Zoom link) | Zhitong Su (Hunan Normal U.) | A decomposition lemma in convex integration via classical algebraic geometry |
| Nov 5 | Huai-Dong Cao (Lehigh) | Hamilton-Ivey-type curvature pinching estimates of Ricci solitons |
| Nov 12 | Charlie Reid (Yale) | Higher Teichmüller theory, and not-so-simple closed curves |
| *Nov 14, 10:30am @ New Brunswick, Hill 705 | Tamás Darvas (Maryland) | A YTD correspondence for constant scalar curvature metrics (*Part of New Brunswick’s Complex Analysis and Geometry Seminar) |
| Nov 19 | Erez Lapid (Weizmann) | Some new results and conjectures about representations of GL_n over a non-archimedean local field (part 1) |
| Nov 26 | No colloquium | Happy Thanksgiving! |
| Dec 3 | Erez Lapid (Weizmann) | Some new results and conjectures about representations of GL_n over a non-archimedean local field (part 2) |
| Dec 10 |
September 17
Minghao Miao (Nanjing University / Rutgers New Brunswick)
The Volume of K-Semistable Fano Manifolds
In 2015, K. Fujita showed that for any n-dimensional K-semistable Fano manifold, the anti-canonical volume is always less than or equal to that of complex projective space (CP^n). In this talk, I will discuss my recent joint work with Chi Li on characterizing the second-largest volume. We prove that for any n-dimensional K-semistable Fano manifold X that is not isomorphic to CPⁿ, the volume is at most 2n^n, with the equality holds if and only if X is a smooth quadric hypersurface or CP^1 × CP^{n-1}. This result applies, in particular, to all Fano manifolds admitting Kähler–Einstein metrics. Our proof is based on a new connection between K-stability and minimal rational curves.
October 1
Alex He (Oklahoma State University)
Practical algorithms in 3-manifold topology
For any fixed compact 3-manifold M, there are infinitely many ways to triangulate M. So given two 3-manifold triangulations, how can we algorithmically decide whether or not they triangulate the same 3-manifold? This is the 3-manifold homeomorphism problem, which is (to say the least) very hard. Nevertheless, we might hope that one day, we can eventually develop a practical algorithm for the homeomorphism problem (that is, an algorithm that is both simple enough to implement in software, and efficient enough that we can actually run the software). This talk will survey some work that has been done to build towards this long-term goal. Specifically, I will discuss some practical algorithms that have been developed to solve some simpler, but still fundamental, problems in low-dimensional topology, such as the problem of computing the prime factorisation of a knot.
October 8
Grace Garden (IMJ-PRG)
Character varieties and essential surfaces
In the seminal work of Culler and Shalen (1983) a method is outlined to detect essential surfaces in a three-manifold by studying their SL(2,C)-character variety. The method underscores connections between the theory of incompressible surfaces in three-manifolds, splittings of fundamental groups, group actions on trees, and the geometry of representation varieties, and led to many developments in low-dimensional topology. In this talk, I will provide an overview of this theory and give intuition through examples. Where possible, I will also discuss recent work extending the theory to algebraically closed fields of arbitrary characteristic. This is joint work with Stephan Tillmann.
October 15
Yikai Teng (Rutgers Newark)
Khovanov homology and exotic planes
Since the 1980s, mathematicians have discovered uncountably many “exotic” embeddings of R2 in R4, i.e., embeddings that are topologically but not smoothly isotopic to the standard xy-plane. However, until today, there have been no direct, computable invariants that could detect such exotic behavior (with prior results relying on indirect arguments). In this talk, we define the end Khovanov homology, which is the first known combinatorial invariant of properly embedded surfaces in R4 up to ambient diffeomorphism. Moreover, we apply this invariant to detect new exotic planes, including the first known example of an exotic plane that is a Lagrangian submanifold of the standard symplectic R4.
October 29
Ao Sun (Lehigh University)
Singular behavior of mean curvature flow
Mean curvature flow describes how a surface evolves to reduce its area as quickly as possible. A central challenge in understanding this flow is the formation of singularities. In this talk, I will discuss recent progress on the singular behavior of mean curvature flow, with a focus on joint work with Zhihan Wang (Cornell) and Jinxin Xue (Tsinghua) on cylindrical singularities.
October 31
Zhitong Su (Hunan Normal University)
A decomposition lemma in convex integration via classical algebraic geometry
We consider a problem of improving the regularity of flexible solutions of a nonlinear PDE, which can be viewed as a kind of linearization of the codimension one local isometric embedding equation in Nash-Kuiper Theorem.
Our approach is based on a decomposition lemma that separates part of the error term arising from convex integration into an elliptic system. The argument involves applications of Adams’ theorem on vector fields on spheres, and classical projective duality. Consequently, our improvement on the Hölder exponent of the solutions depends on the Radon-Hurwitz number, exhibiting an eightfold periodicity that reflects Bott periodicity. This is joint work with Weijun Zhang.
November 5
Huai-Dong Cao (Lehigh)
Hamilton-Ivey-type curvature pinching estimates of Ricci solitons
A magic feature of the Ricci flow in three dimensions is the well-known Hamilton–Ivey curvature pinching estimate. Roughly speaking, it asserts that when the curvature blows up along the 3D Ricci flow, the positive part blows up at a faster rate than (absolute value of) the negative part. As a consequence, all 3D shrinking or steady gradient Ricci solitons (or more generally, ancient solutions) arising as limits of parabolic blowups of the flow must have nonnegative sectional curvature. This is extremely powerful in the analysis of 3D Ricci flow singularity models, as it enables the effective use of the Li–Yau–Hamilton differential Harnack inequality and the geometry of non-negatively curved three-manifolds.
In recent years, various generalizations of Hamilton–Ivey curvature pinching have been developed for general shrinking and steady Ricci solitons, and more broadly, for ancient solutions, in both dimension three and higher dimensions. In this talk, I will discuss some new progress on Hamilton–Ivey-type curvature pinching for gradient Ricci solitons, based on my joint work with Junming Xie.
November 12
Charlie Reid (Yale)
Higher Teichmüller theory, and not-so-simple closed curves
A hyperbolic structure on a surface is captured by a representation of the fundamental group into PSL(2,R). Higher rank Teichmüller theory aims to go beyond hyperbolic geometry by studying representations into bigger lie groups, for instance PSL(n,R). I will discuss a “higher” version of one piece of hyperbolic geometry–Thurston’s compactification of Teichmüller space. Boundary points of this compactification are measured laminations, measure-theoretic objects generalizing simple closed curves. I will discuss compactifications of certain higher Teichmüller spaces where we will see closed curves with more intricate restrictions on self-intersection appearing in the boundary.
Bonus: November 14 (at New Brunswick)
Tamás Darvas (University of Maryland)
A YTD correspondence for constant scalar curvature metrics
Given a compact Kähler manifold, to better understand Mabuchi’s K energy we introduce a family of K^beta energies, whose favorable properties are similar to those of the Ding energy from the Fano case. The construction uses Berman’s transcendental quantization, and we show that the slope of the K^beta energies along test configurations can be computed using intersection theory. With these ingredients in place we provide a uniform Yau-Tian-Donaldson correspondence that characterizes the existence of a unique constant scalar curvature Kähler metric using test configurations. Combining our techniques with the non-Archimedean approach to K-stability pioneered by Boucksom-Jonsson, we show that the properness of the classical energy can be tested by checking its slope along a distinguished subclass of Li-type models, called log discrepancy models, thus yielding another G-uniform Yau–Tian–Donaldson correspondence. (Joint with Kewei Zhang)
November 19 (part 1) & December 3 (part 2)
Erez Lapid (Weizmann Institute of Science)
Some new results and conjectures about representations of GL_n over a non-archimedean local field
The seminal work of Joseph Bernstein and Andrei Zelevinsky in the 1970s on representation theory of GL_n over a non-archimedean local field culminated in Zelevinsky’s classification of the irreducible ones in terms of mysterious objects and seemingly innocuous combinatorial objects. The latter have rich geometric structure and show up in other contexts of representation theory such as Lustzig’s canonical bases.
In my talks I will present recent progress on understanding the composition series, and in particular the reducibility, of parabolic induction of representations of general linear groups. The study leads to new geometric constructions in the context of Lusztig’s nilpotent varieties and new relations to classical combinatorial constructions such as the RSK correspondence. I will strive to keep the talks self-contained and logically independent of each other.
Based on joint works with Alberto Minguez, Rami Aizenbud and Max Gurevich.
Schedule — Spring 2025
| Date | Speaker | Title |
|---|---|---|
| Jan 29 | No talk | |
| Feb 5 | No talk | |
| Feb 12 | No talk | |
| Feb 19 | Federico Ardila (San Francisco State) | Inequalities for trees and matroids |
| Feb 26 | No talk | |
| Mar 5 | Zhaolin Li (University of Minnesota) | Beyond Endoscopy: Standard L-functions of GL(2) |
| Mar 12 | Botong Wang (University of Wisconsin) | Homology classes of surfaces in (P1)4 |
| Mar 19 | No talk | Spring break |
| Mar 26 | Jie Gao (Rutgers NB) | Discrete Ricci flow and Applications on Graph Analysis |
| Mar 31 (Monday) | Alejandro H. Morales (Université du Québec à Montréal) | Enumerating factorizations: from the symmetric group to Hecke algebras |
| Apr 2 | Kasia Jankiewicz (UC Santa Cruz) | Approximating Artin groups by their finite quotients |
| Apr 9 | Griffin Wang (IAS) | Geometrization of the Jacquet-Rallis Fundamental Lemma for Spherical Hecke Algebras |
| Apr 16 | Chi Li (Rutgers NB) | Two uniqueness results in Kahler geometry |
| Apr 23 | Gongxiang Liu (Nanjing University) | On the classification of graded pointed coquasi-Hopf algebras over finite abelian groups. |
| Apr 30 | Zhiyu Zhang (Standford) |
Schedule — Fall 2024
| Date | Speaker | Title |
|---|---|---|
| Sep 11 | Baiqing Zhu Columbia University |
Intersection of Hecke correspondences on modular curves |
| Sep 18 | TBA | TBA |
| Sep 25 | Qiao He Columbia University |
Kudla–Rapoport conjecture at bad reduction primes |
| Oct 2 | TBA | TBA |
| Oct 9 | Diana Hubbard CUNY |
Twisting in mapping class groups |
| Oct 16 | Yu-Shen Lin Boston University |
Construction of Special Lagrangians in Collapsing Limits |
| Oct 22 (Special date!) |
Junliang Shen Yale University |
The D-equivalence conjecture and hyper-Kähler geometry |
| Oct 30 | Junyan Zhao University of Maryland |
Degree of curves and measures of irrationality |
| Nov 4 | Kate Petersen University of Minnesota–Duluth |
Please check https://sites.rutgers.edu/dltg/lectures/ for more details |
| Nov 6 | Caleb Suan The University of British Columbia |
Long-Time Existence of the Anomaly Flow |
| Nov 13 | Weixiao Lu MIT |
TBA |
| Nov 18 | Marina Ville University of Tours, France |
Please check https://sites.rutgers.edu/dltg/lectures/ for more details |
| Nov 20 | TBA | TBA |
| Nov 27 | Thanksgiving! | No talk |
| Dec 4 | Alina Vdovina CUNY |
Knots, surfaces and complexity |
| Dec 11 | Zhilin Luo University of Chicago |
Nonabelian Fourier analysis in Langlands program |
Schedule — Spring 2023
| Date | Speaker | Title |
|---|---|---|
| Jan 25 | Chongying Dong (UC Santa Cruz) — Virtual meeting | Monstrous moonshine and vertex operator algebras |
| Feb 1 | Zahi Hazan (Tel Aviv University) | An Identity Relating Eisenstein Series on General Linear Groups |
| Feb 8 | No talk | |
| Feb 15 | 1st talk: Dihua Jiang (University of Minnesota) 2nd talk: Ralph Kaufmann (Purdue University) |
Arithmetic Wavefront Set, Local Descent, and Local Gan–Gross–Prasad Conjecture Algebra and geometry from graphs |
| Feb 22 | Ziming Shi (Rutgers–NB) Ziquan Zhuang (JHU) |
1/2 estimate for global Newlander–Nirenberg theorem on strongly pseudoconvex domains Stability and boundedness of klt singularities |
| Mar 1 | Jialiang Zou (University of Michigan) | Arthur’s multiplicity formula and local Langlands correspondence for (special) orthogonal and unitary groups via theta lifts |
| Mar 8 | 1st talk: Luen-Chau Li (PSU) 2nd talk: Ping Xu (PSU) |
On infinite periodic band matrices and the periodic Toda flow Introduction to deformation quantization |
| Mar 15 | No talk (Spring break) | |
| Mar 22 | Huajie Li (JHU) | Introduction to the relative trace formulae of Guo–Jacquet |
| Mar 29 | Hannah Schwartz (Princeton) — Cancelled | Gluck Twisting 2-Spheres |
| Apr 5 | Ian Morrison (Fordham) | The poset of $0$-$1$ factorizations of $\frac{1-x^n}{1-x}$ |
| Apr 12 | Stephan Tillmann (The University of Sydney) | Three angles on tropical geometry |
| Apr 19 | Mark McLean (Stony Brook) | Floer Cohomology and Arc Spaces |
| Apr 26 | Anna Wienhard (Mathematisches Institut, Ruprecht-Karls-Universität Heidelberg) | Positivity, representations, and non-commutative hyperbolic geometry |
| May 3 | Yanwen Luo (Rutgers–NB) | Drawing and Morphing Graphs on Surfaces |
Schedule — Fall 2021 – Spring 2022
| Date | Speaker | Title |
|---|---|---|
| Sep 15 | No talk | |
| Sep 22 | No talk | |
| Sep 29 | Wenshuai Jiang (Zhejiang University) | Gromov-Hausdorff limit of manifolds and some applications |
| Oct 6 | Kewei Zhang (Beijing Normal University) | Moser-Trudinger type inequalities on compact Kahler manifolds |
| Oct 13 | Freid Tong (Harvard) | Uniform estimates for complex Monge-Ampere and fully nonlinear equations |
| Oct 15 | Yiannis Sakellaridis (Johns Hopkins University) | Periods, L-functions, and a duality of Hamiltonian spaces |
| Oct 20 | Naihuan Jing (NC State University) | Yangians and their presentations |
| Oct 27 | No talk | |
| Nov 3 | No talk | |
| Nov 10 | Spencer Leslie (Duke University) | Periods of automorphic forms and endoscopy |
| Nov 17 | Qingyuan Jiang (The University of Edinburgh) | Derived projectivizations of two-term complexes |
| Nov 24 | No Talk. Happy Thanksgiving! | |
| Dec 1 | Chengming Bai (Nankai University) | An introduction to pre-Lie algebras with some recent progress |
| Dec 8 | Sylvie Paycha (Universität Potsdam) | From principal bundles with connections to groupoids with direct connections: the case of jet groupoids |
| Jan 18 | Kyle Hayden (Columbia University) | Braids and badly behaved surfaces |
| Jan 20 | Christine Ruey Shan Lee (University of South Alabama) | Quantum knot invariants and low-dimensional topology |
| Jan 24 | Vesselin Dimitrov (University of Toronto) | Is there a smallest algebraic integer? |
| Jan 25 | Ying Anna Pun (University of Virginia) | Symmetric functions — a gem in algebraic combinatorics |
| Jan 27 | Andrea Tamburelli (Rice University) | Thurston boundary for higher Teichmuller spaces |
| Feb 16 | Marc Lackenby (University of Oxford) | Recognising the unknot |
| Feb 23 | Bin Zhang (Sichuan University) | Renormalization of Feynman amplitudes on Riemannian manifolds |
| Mar 2 | Wen-Wei Li (Peking University) | Differential operators in representation theory for Lie groups |
| Mar 9 | Radmila Sazdanovic (NC State University) | Linearizations of category of 2D cobordisms and generalizations of the Deligne category |
| Mar 16 | No talk. Happy spring break! | |
| Mar 23 | Boyu Zhang (Princeton University) | The smooth closing lemma for area-preserving surface diffeomorphisms |
| Mar 30 | Ao Sun (University of Chicago) | Dynamics of Singularities of Mean Curvature Flow |
| Apr 6 | Bin Xu (Tsinghua University) | ABV-packets for unramified principal series of p-adic general linear groups and Lusztig’s semicanonical bases |
| Apr 13 | Xin Fu (UC Irvine) | Neck region in geometric problems |
| Apr 20 | Chao-Ming Lin (UC Irvine) | The deformed Hermitian—Yang—Mills equation, the Positivstellensatz, and the Solvability |
| Apr 27 | William Goldman (University of Maryland) | Dynamics and the classification of geometric structures on surfaces |