Colloquia



Our department is proud to host weekly colloquium talks featuring research by leading mathematicians from around the world. Most colloquia are held on Fridays at 4pm in ACLC, Room 010 (unless otherwise advertised) with refreshments preceding at 3:15pm in Parker Hall, Room 244. 

Upcoming Colloquia
DMS Colloquium: Dr. Xiaolong Li

Apr 10, 2025 03:30 PM

PLEASE NOTE: DAY--THURSDAY, April 10 and TIME--3:30 (refreshments in 244 Parker at 3:00)
 
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Speaker: Dr. Xiaolong Li (Wichita State University) 
 
Title: Geometry and Analysis of Einstein Four-manifolds 
 
 
Abstract: Einstein manifolds are fundamental objects in differential geometry, with deep connections to general relativity and mathematical physics. Their natural generalizations—quasi-Einstein manifolds or Ricci solitons—play a crucial role in the study of geometric flows, particularly Ricci flow. While Einstein metrics in low dimensions (two and three) are well understood, their classification in dimensions higher than four appears intractable. However, dimension four occupies a unique and intriguing position: it is rich enough to exhibit intricate geometric and topological phenomena, yet still accessible to classification efforts under suitable conditions. In this talk, I will survey some key developments in the study of Einstein metrics on four-manifolds, highlighting known examples and classification results. I will also mention some outstanding open problems and promising directions for future research.
 
The talk is based on a joint survey with Xiaodong Cao (Cornell) and Hung Tran (Texas Tech).
 

Recent Colloquia
DMS Colloquium: Dr. Minjae Park

Mar 20, 2025 03:30 PM

Refreshments at 3:00 in 244 Parker Hall
 
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Speaker: Dr. Minjae Park (University of Chicago). 
 
​Title: Geometry of uniform meandric systems 
 
 
Abstract: I will discuss how a random geometry perspective can provide new insights into classical combinatorial objects, using meandric systems as an example. A meandric system of size n consists of loops formed by two arc diagrams—non-crossing perfect matchings on {1,…,2n}—with one drawn above and the other below the real line. Equivalently, it is a coupled collection of meanders with a total size of n. I will present a conjecture describing the large-scale geometry of a uniformly sampled meandric system of size n in terms of Liouville quantum gravity (LQG) surfaces decorated by Schramm-Loewner evolution (SLE)-type curves. I will then outline several rigorous results supporting this conjecture. In particular, a uniform meandric system exhibits macroscopic loops; and its half-plane version has no infinite paths.
 
The results are based on joint work with Jacopo Borga (MIT) and Ewain Gwynne (UChicago). ​
 
​If time permits, I will also discuss connections between this approach and other probabilistic structures, such as permutons (limits of permutations), the directed landscape, and other conformal field theory models. ​
 

DMS Colloquium: Dr. Graeme Milton

Feb 28, 2025 02:00 PM

Update: The colloquium has been rescheduled to 2pm (still in Parker 328); refreshments will be served at 1:30pm.

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Speaker: Dr. Graeme Milton (University of Utah)

Title: Guiding Stress: From Pentamodes to Cable Webs to Masonry Structures 

 

Abstract: Pentamode materials are a class of materials that are useful for guiding stress. In particular, they have been proposed for acoustic cloaking by guiding stress around objects and have been physically constructed.  A key feature of pentamode materials is that each vertex in the material is the junction of 4 double cone elements. Thus, the tension in one element determines the tension in the other elements, and by extension, uniquely determines the stress in the entire metamaterial. Here we show how this key feature can be extended to discrete wire networks, supporting forces at the terminal nodes, and which may have internal nodes where no forces are applied. In usual wire or cable networks, such as in a bridge or bicycle wheel, one distributes the forces by adjusting the tension in the wires. Here our discrete networks provide an alternative way of distributing the forces through the geometry of the network. In particular, the network can be chosen so it is uniloadable, i.e., supports only one set of forces at the terminal nodes. Such uniloadable networks provide the natural generalization of pentamode materials to discrete networks. We extend such a problem to compression-only "strut nets" subjected to fixed and reactive nodal loads. These systems provide discrete element models of masonry bodies.  In particular, we solve the arch problem where one wants the strut net to avoid a given set of obstacles, and also allow some of the forces to be reactive ones.

 

This is joint work with Ada Amendola, Guy Bouchitté,  Andrej Cherkaev, Antonio Fortunato, Fernando Fraternali, Ornella Mattei, and Pierre Seppecher.


DMS Colloquium: Dr. Songling Shan

Feb 21, 2025 03:30 PM

Refreshments will be served in Parker 244, 3-3:25pm.
 
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Speaker: Dr. Songling Shan (Auburn) 
 
Title: Graph Edge Decomposition and Graph Toughness 
 
 
Abstract:  This talk focuses on our recent work in two areas of graph theory: edge decomposition into non-conflicting groups and Hamiltonian cycles under toughness conditions. I will present an overview of several conjectures in the areas and discuss some partial results we have obtained.
 
This talk is a part of Dr. Shan's 3rd year review process. 
 

DMS Colloquium: Dr. Justin Lyle

Jan 31, 2025 01:00 PM

(Refreshments will be served in Parker 144 after the talk)
 

Speaker: ​ Dr. Justin Lyle (Auburn University)

Title: Homological Aspects of Commutative Rings 

 

Abstract: Homological methods have been integral to our understanding of both commutative and noncommutative algebras since the so-called "Homological Invasion" of the 1950's and have led to solutions of numerous problems not intrinsically homological in nature. Despite this, there are several fundamental aspects that remain mysterious, with several problems from the 1950s-1970s remaining stubbornly open, including the Finitistic Dimension Conjecture, the Nakayama Conjecture and its generalized variant, the Tachikawa Conjectures, and the Auslander-Reiten Conjecture. In this talk, we give an overview of the historical and broader contexts of these problems and discuss recent progress of the speaker on some related questions, as a consequence leading to new broad cases of the Auslander-Reiten conjecture.


DMS Colloquium: ​Dr. Prashanth Sridhar

Jan 29, 2025 01:00 PM

(Refreshments will be served in Parker 144 after the talk)
 

Speaker: ​Dr. Prashanth Sridhar (Auburn University) 

Title: Differential Graded Noncommutative Geometry 

 

Abstract: Pioneering work of Artin-Tate-Van den Bergh-Zhang extends important aspects of projective geometry to the noncommutative (nc) setting. In particular, the derived category of such a nc scheme shares many features with the derived category of a classical one. In this talk, I'll discuss extensions of some classical and modern results in the theory of nc projective geometry to nc spaces associated to dg-algebras. The focus will be on applications to projective varieties.

 

DMS Colloquium: Dr. Ji Li

Nov 25, 2024 03:30 PM

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Speaker: Dr. Ji Li (Macquarie University; Sydney, Australia)

Title: Schatten properties of Riesz transform commutator in the two weight setting

 

Abstract. Schatten class estimates of the commutator of Riesz transform in \({\mathbb{R}}^n\) link to the quantised derivative of A. Connes. A general setting for quantised calculus is a spectral triple \((\mathcal{A, H, D})\), which consists of a Hilbert space \({\mathcal{H}}\), a pre-\(C^∗\)-algebra \({\mathcal{A}}\), represented faithfully on \({\mathcal H}\) and a self-adjoint operator \({\mathcal D}\) acting on \({\mathcal{H}}\) such that every \(a ∈ A\) maps the domain of \({\mathcal D}\) into itself and the commutator \([D, a] = Da−aD\) extends from the domain of \({\mathcal D}\) to a bounded linear endomorphism of \({\mathcal{H}}\). Here, the quantised differential \da of \(a ∈ A\) is defined to be the bounded operator \(i[sgn(D), a]\), \(i2 = −1\).


We provide full characterisation of the Schatten properties of \([Mb, Rj ]\), the commutator of the \(j\)-th Riesz transform on \(R^n\) with symbol \(b (Mbf(x) := b(x)f(x))\), in the two weight setting. The approach is not depending on the Euclidean structure or Fourier, and hence it can be applied to other settings.


This talk is based on my recent work joint with Michael Lacey, Brett Wick, and Liangchuan Wu.