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September 2021

Chenyang Xu, Princeton – Mathematics Colloquium

September 9, 2021 @ 4:00 pm - 5:00 pm

Speaker: Chenyang Xu,  Princeton Time: 4:00 pm Over Zoom Title: Canonical metrics, stability and moduli space Abstract: In the last half century, the interplay between canonical metrics and stability for various algebraic objects has been a central topic in geometry. Many new theories are developed to understand each side, as well as their relation. In my talk, I will survey the recent progress on one example of this kind: the complete solution of the Yau-Tian-Donaldson Conjecture for varieties with a…

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October 2021

Lilian Pierce, Duke University – Mathematics Colloquium

October 28, 2021 @ 4:00 pm - 5:00 pm

Lilian Pierce, Duke University Mode: Zoom Time: 4:00 pm - 5:00 pm Virtual Tea-time starting at 3:45pm Title: Counting problems: open questions in number theory Abstract: Many questions in number theory can be phrased as counting problems. How many primes are there? How many elliptic curves are there? How many integral solutions to this system of equations are there? How many number fields are there? Sometimes the answer is “infinitely many,” and then we want to understand the order of…

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November 2021

David Nadler, UC Berkley – Mathematics Colloquium

November 4, 2021 @ 4:00 pm - 5:00 pm

Location: Phillips Hall, Room 332 Tea-time starting at 3:30 pm in Phillips Hall, Room 330 Time: 4:00 pm – 5:00 pm Speaker: David Nadler, UC Berkeley Title: Skeleta of Weinstein manifolds Abstract: I'll survey some history and motivation for the study of Weinstein manifolds and their skeleta. Then I'll discuss recent and ongoing work with Dani Alvarez-Gavela and Yasha Eliashberg devoted to understanding polarized Weinstein manifolds in terms of their skeleta.

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Greg Forest, UNC-Chapel Hill – Joint Mathematics-Applied Mathematics Colloquium

November 11, 2021 @ 4:00 pm - 5:00 pm

UNC Mathematics-Applied Mathematics Joint Colloquium Speaker: Greg Forest, UNC Chapel Hill Time: 4pm Mode: In-person - Phillips Hall 332 tea-time in Phillips Hall 330 at 3:30 pm Title: Modeling insights into SARS-CoV-2 respiratory tract infections Abstract: I and many collaborators, postdocs, and students from many disciplines have explored lung mechanics and disease pathology for over 2 decades in a pan-university effort called the UNC Virtual Lung Project. In the last decade with the Sam Lai lab we have explored how…

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Dima Arinkin, University of Wisconsin, Madison – Mathematics Colloquium

November 18, 2021 @ 4:00 pm - 5:00 pm

Mode: Zoom Title: Moduli spaces and their compactifications Abstract: Very broadly speaking, geometry is the study of spaces. Here `space' is a  placeholder: different flavors of geometry work with spaces such as differentiable manifolds (differential geometry), topological spaces (topology), varieties (algebraic geometry, my favorite), and so on. But what makes a space an interesting object of study? One class of `interesting' spaces is the so-called moduli spaces (the word `moduli' goes back to Riemann and means `parameters'). Moduli spaces parametrize objects of…

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February 2022

Lisa Piccirillo, MIT – Mathematics Colloquium

February 10 @ 4:00 pm - 5:00 pm

Mode: Zoom only Virtual tea at 3:45pm Title: Knot concordance and 4-manifolds Abstract: There is a rich interplay between the fields of knot theory and 3- and 4-manifold topology. In this talk, I will describe a weak notion of equivalence for knots called concordance, and highlight some historical and recent connections between knot concordance and the study of 4-manifolds, with a particular emphasis on applications of knot concordance to the construction and detection of small 4-manifolds which admit multiple smooth…

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Ken Ono – Mathematics Colloquium Talk

February 24 @ 4:00 pm - 5:00 pm

Mode: Virtual only Virtual Tea-time at 3:45 pm Title: New results in arithmetic statistics Abstract:  Studying the statistical behavior of number theoretic quantities is presently in vogue. This lecture will begin with a new look at classical results in number theory from the perspective of arithmetic statistics, which then naturally lead to point counts for elliptic curves and K3 surfaces over finite fields. This lecture will use the celebrated Sato-Tate Conjecture (now theorem thanks to Richard Taylor and his collaborators) as motivation…

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March 2022

Ivan Loseu, Yale University – Mathematics Colloquium

March 24 @ 4:00 pm - 5:00 pm

Title: Unipotent representations and quantization. Abstract: A fundamental question in the representation theory of semisimple Lie groups is to classify their irreducible unitary representations. A guiding principle here is the Orbit method, first discovered by Kirillov in the 60's for nilpotent Lie groups. It states that the irreducible unitary representations should be related to coadjoint orbits, i.e., the orbits of the Lie group action in the dual of its Lie algebra. Passing from orbits to representations could be thought of…

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April 2022

Tamas Hausel, IST Austria – Mathematics Colloquium

April 7 @ 2:00 pm - 3:00 pm

Time: Thursday, April 7th, 2:00 pm - 3:00 pm Mode: Zoom Title: Ubiquity of systems of homogenous polynomial equations with a unique solution Abstract: Following Macaulay we will analyse systems of equations as in the title leading to marvelous properties of its multiplicity algebra. Examples include isolated surface singularities, equivariant cohomology and fixed point sets of group actions as well as the Hitchin integrable system on very stable upward flows.  

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Andrei Negut, MIT – Mathematics Colloquium

April 14 @ 4:00 pm - 5:00 pm

Mode: In-person Title: Quantum algebras, shuffle algebras and Hall algebras Abstract: The Hall algebra of coherent sheaves on a genus g curve over F_q is an important object in geometric representation theory: when g=0 it gives rise to the positive half of U_q(Lsl_2), while its g=1 case (known as the elliptic Hall algebra) has recently found numerous applications, ranging from the study of categorical knot invariants to the study of derived categories of Hilbert schemes of surfaces. In the present…

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