TADS is a venue for presentation/discussion concerning
topology, algebraic geometry, or dynamics (broadly understood).
Attendance is open, and those interested in giving a talk should e-mail title/abstract to any committee member (dcarched, or alukyane at
gmu.edu). Talks are 50-90 minutes, and will, for the time being, take place on Zoom:
ZOOM LINK.
TADS Committee: David Carchedi (chair), Anton Lukyanenko
Fall 2020: Fridays 1:30-3:00 PM
Friday, December 4, 2020
Notre Dame, Pavel Mnev
We study the perturbative path integral of Chern-Simons theory on a cylinder [0,1]x Sigma with a holomorphic polarization on the boundaries, in the context of Batalin-Vilkovisky quantization (or rather its variant compatible with cutting-gluing, the “BV-BFV quantization”). We find that, in the case of non-abelian 3D Chern-Simons, the fiber BV integral for the system produces the gauged WZW model on Sigma. Classically, the result corresponds to computing a “generalized Hamilton-Jacobi action” for Chern-Simons theory on a cylinder — a generating function (in an appropriate sense) for the evolution relation induced on the boundary conditions by the equations of motion. A similar setup applied to 7D abelian Chern-Simons on a cylinder [0,1] x Sigma, with Sigma a Calabi-Yau of (real) dimension 6, with a linear polarization on one side and a nonlinear (Hitchin) polarization on the other side, is related to the Kodaira-Spencer (a.k.a. BCOV) theory.
In the talk, I will introduce the concept of generalized Hamilton-Jacobi functions in the example of classical mechanics with constraints described by an equivariant moment map and proceed to discuss the examples above. This is a report on a joint work with Alberto S. Cattaneo and Konstantin Wernli.
Friday, November 20, 2020
Cary Malkiewich, Binghamton University
Abstract: In this talk I will discuss various lifts of the characteristic polynomial to the setting of algebraic K-theory, and describe the relationship to trace methods and to topological fixed-point theory and dynamics.
November 13, 2020
Theo Johnson-Freyd, Dalhousie University, Perimeter Institute
Abstract: I will explain how some questions in theoretical physics and algebraic topology led to a curious result about error-correcting ternary codes. No knowledge of the terms in the title or abstract will be assumed. Based on joint work with Davide Gaiotto.
Spring 2020
February 28, 2020
Akhil Mathew, University of Chicago
Given a smooth algebraic variety X over C, a classical result of Grothendieck shows that one can recover the singular cohomology of X (with complex coefficients) using only algebraic differential forms. In characteristic p, the analogous construction also works but is less satisfactory: it produces only p-torsion cohomology groups. The de Rham-Witt complex (or crystalline cohomology) provides an integral lift, and yields one of the basic cohomology theories for varieties in characteristic p. In this talk, I will explain a new approach to the de Rham-Witt complex based only on elementary homological algebra. Joint work with Bhargav Bhatt and Jacob Lurie.
February 21, 2020
Owen Gwilliam, UMass Amhrest
Factorization homology arises in algebraic topology as a nonlinear generalization of homology theory a la Eilenberg-Steenrod. The first part of my talk will focus on developing the notions of factorization algebra and factorization homology, as articulated by Ayala-Francis and Lurie. In the second part I will discuss how factorization algebras arise naturally in classical and quantum field theory. The goal is to explain recent joint work with Eugene Rabinovich and Brian Williams about field theory on manifolds with boundary, which offers a useful perspective on Kontsevich's deformation quantization of Poisson manifolds as well as the relationship of loop groups to quantum groups via perturbative Chern-Simons theory.
February 7, 2020
Suhyoung Choi, KAIST
We give some introduction to the field of complete affine n-manifolds, ,i.e., quotients of the affine n-space by properly discontinuous actions of affine transformation groups.
We will try to show that closed manifolds of negative curvature do not admit complete special affine structures whose linear parts are partially hyperbolic in the dynamical sense. We can drop the negative curvature condition. We present our attempt here. (Partially a joint work with Kapovich.)
Fall 2019
December 6, 2019
Grace Work, Girls' Angle and M.I.T.
Abstract: Consider a nested family of target sets shrinking at a specified rate and a given flow, we want to understand the set of points whose orbits hit these targets infinitely often under the flow. One way to examine this set is to determine under what conditions this set has full measure. This question is closely related to the Borel-Cantelli Lemma and also gives rise to logarithm laws. In joint work with Spencer Dowdall we examine this particular question for Teichmuller flow on the moduli space of unit-area quadratic differentials.
November 22, 2019
Elizabeth Milicevic, Haverford College
November 15, 2019
Julianna Tymoczko, Smith College
November 1, 2019
Brent Gorbutt, George Mason University
October 18, 2019
Changlong Zhong, SUNY Albany
October 4, 2019
Anders Buch, Rutgers University
September 20, 2019
Leonardo Mihalcea, Virginia Tech
September 6, 2019
Andrei Rapinchuk, University of Virginia
Spring 2019
April 26, 2019
Polygon Spaces
Jack Love, George Mason University
April 19, 2019
Special nilpotents and Higher Teichmüller spaces
Brian Collier, University of Maryland, College Park
April 5, 2019
Expanding Thurston maps and visual spheres
Annina Iseli, University of California, Los Angeles
March 22, 2019
Capturing invariance in flows and combinatorial vector
fields
Tom Wanner, George Mason University
March 8, 2019
Singularities of commutative rings via test ideals
Rebecca R.G., George Mason University
February 22, 2019
Dynamics and the Clebsch diagonal cubic surface
William Goldman, University of Maryland, College Park
February 8, 2019
How self-driving robots find delivery paths, and how this leads to sub-Riemannian geometry
Anton Lukyanenko, George Mason University
January 25, 2019
Explicit modular forms via the homotopy groups of spheres.
Donald Larson, Catholic University of America
Fall 2018
November 30, 2018
Convex hulls of quasicircles in hyperbolic and anti-de Sitter space
Sara Maloni, University of Virginia
November 16, 2018
Battle Hymn of Discreteness
Caleb Ashley, University of Michigan
November 2, 2018
On some (equivariant) combinatorics related to flag
manifolds
Rebecca Goldin, GMU
October 26, 2018
Quasi-isometries of the Baumslag-Gersten group
Tullia Dymarz, University of Wisconsin–Madison
September 28, 2018
Toric Vector Bundles and Piecewise Linear Maps
Christopher Manon, University of Kentucky
September 14, 2018
Ergodicity of Iwasawa continued fractions via markable hyperbolic geodesics
Anton Lukyanenko, GMU
Spring 2018
April 27, 2018
Morse theory and a stack of broken lines
Hiro Lee Tanaka, Harvard University
April 6, 2018
Topological realization of varieties over Spec C((t)) via log
geometry
Mattia Talpo, Simon Fraser University
April 6, 2018
Connecting Outreach and Continued Fraction Expansions Through Tessellations
Claire Merriman, UIUC
Special Time: 4:40-5:30pm
March 30, 2018
Representation stability, homological stability, and
commuting matrices
Daniel Ramras, Indiana University–Purdue University Indianapolis
March 2, 2018
Hilbert Schemes and the Motivic Sphere Spectrum
Elden Elmanto, Northwestern University
February 23, 2018
Homotopy types of moduli spaces of foliations
David Carchedi, GMU
February 16, 2018
Some results on affine Deligne-Lusztig varieties
Xuhua He, UMCP
February 9, 2018
How to do Multivariable Calculus on Graphs
Tyrus Berry, GMU
January 23, 2018
Poisson Structure on Compactification of Moduli Space of
Representations
Sean Lawton, GMU
Fall 2017
November 17, 2017
Lipschitz maps from PI spaces to Carnot groups
Kyle Kinneberg
October 20, 2017
Dirichlet domains in different geometries
Todd Drumm, Howard University
October 13, 2017
Homotopy types as a foundation for mathematics
Emily Riehl, JHU
October 6, 2017
Counting matrices with forced zero entries
Joel Lewis, George Washington University
September 22, 2017
An invitation to the Heisenberg group and its deformations
Anton Lukyanenko, GMU
September 15, 2017
Free products and regularity of group actions
Thomas Koberda, UVA
September 8, 2017
Can rotation numbers be computed from a quasiperiodic trajectory?
Evelyn Sander, GMU
Spring 2017
May 5, 2017
Hyperbolic localization and nearby cycles
Tom Haines, UMCP
April 14, 2017
The Erdos-Szekeres Problem
Valeriu Soltan, GMU
April 7, 2017
Quotient of surface groups and homology of finite covers
via Topological Quantum Field Theories
Ramanujan Santharoubane, University of Virginia
March 24, 2017
Invertible Orbifolds over Finite Fields
Marco Aldi, Virginia Commonwealth University
March 10, 2017
Accessing Geometry via Function Spaces
Tyrus Berry, GMU
March 3, 2017
Manifolds, Schemes, Deligne-Mumford stacks, and
Orbifolds: Why they’re all topoi.
David Carchedi, GMU
February 17, 2017
Tropical geometry of complexity 1 T -varieties
Chris Manon, GMU
February 10, 2017
Families of Unitary Representations and Kazhdan’s Property (T)
Dan Ramras, IUPUI
February 3, 2017
Compactification of Character Varieties
Sean Lawton, GMU
January 27, 2017
An introduction to 2−Segal spaces
Julie Bergner, UVA
Fall 2016
December 15, 2016
Tropicalization of Configurations of Flags
Ian Le, Perimeter Institute for Theoretical Physics
Special Date/Location: 12/15/16, Fishbowl (4th floor of Exploratory Hall)
December 9, 2016
Operads with homological stability
Sarah Yeakel, University of Maryland
December 2, 2016
SO(p, q)-surface group representations
Brian Collier, University of Maryland
October 28, 2016
Parabolic Higgs Bundles & Generalized Parabolic Higgs
Bundles
Marina Logares, Oxford
October 21, 2016
Polyhedra inscribed in quadrics and their geometry
Sara Maloni, University of Virginia
October 14, 2016
Schottky groups and maximal representations
Jean-Philippe Burelle, University of Maryland
September 30, 2016
How to make 3-D printed sculptures of 4-D things. (Public Lecture)
Henry Segerman, Oklahoma State University
Special Location and Time: The HUB Ballroom, 2-3pm presention, 3-4pm book-signing.
September 16, 2016
Introduction to hyperrings and hyperfields
Jaiung Jun, Binghamton University
Spring 2016
May 20, 2016
Positivity in Schubert Calculus, Part 2
Rebecca Goldin, George Mason University
May 13, 2016
Rank 1 Character Varieties
Sean Lawton, George Mason University
April 29, 2016
Positivity in Schubert Calculus
Rebecca Goldin, George Mason University
April 15, 2016
Geometry of the Vinberg’s Enveloping Monoid
Chris Manon, George Mason University
March 21, 2016
Voronoi Tilings and Loop Groups
Pablo Solis
, CalTech
March 18, 2016
Algebraic Vision: the Quadrifocal Variety
Luke Oeding, Auburn University
March 4, 2016
The Gauss map and Diophantine approximation in the
Heisenberg group
Anton Lukyanenko, University of Michigan
February 19, 2016
Genus of complete intersections in spherical varieties
Kiumars Kaveh, University of Pittsburgh
February 5, 2016
Strange duality of non-abelian theta functions
Swarnava Mukhopadhyay, University of Maryland, College Park
Fall 2015
December 18, 2015
Higgs bundles at the Fuchsian locus
Richard Wentworth, University of Maryland, College Park
December 4, 2015
Algebraic Properties of Skein Algebras of Surfaces
Adam Sikora, State University of New York at Buffalo
November 13, 2015
Stable Representation Theory and Spaces of Flat Connections
Daniel Ramras, Indiana University-Purdue University Indianapolis
November 6, 2015
A new approach to etale homotopy theory
David Carchedi, GMU
October 30, 2015
Geometry and Connectivity of Space of Finite Unit-Norm
Tight Frames
Nate Strawn, Georgetown
October 9, 2015
Coordinates for representations of 3-manifold groups
Christian Zickert, University of Maryland, College Park
September 25, 2015
How to pinch a neck on a convex RP2 surface.
John Loftin, Rutgers-Newark
Summer 2015
July 24, 2015
Tropical computational experiments with compactifications of the deformation spaces of convex real projective structures on 2-orbifolds and surfaces
Suhyoung Choi, Korean Advanced Institute of Science and Technology (KAIST)
Spring 2015
April 24, 2015
The space of local overrings of an integral domain
Neil Epstein, George Mason University
April 10, 2015
Equations of tropical varieties
Jeffrey Giansiracusa, Swansea University
March 6, 2015
Proper affine deformations of the one-holed torus
Todd Drumm, Howard University
February 27, 2015
Zeta functions and motivic measures
Niranjan Ramachandran, University of Maryland
February 13, 2015
Complex dynamics and elliptic curves
Laura DeMarco, Northwestern University
January 30, 2015
Representation theory of symplectic singularities
Ben Webster, University of Virginia
Fall 2014
December 3, 2014
Primitive Geodesic Lengths and Arithmetic Progressions
Ben McReynolds, Purdue University
Special Time: 5-6pm
November 19, 2014
Tameness of Margulis Spacetimes
William Goldman, University of Maryland
November 12, 2014
Homotopy of Character Varieties
Sean Lawton, George Mason University
October 29, 2014
The geometry of Euclidean polygons
Chris Manon, George Mason University
October 15, 2014
Counting Points on a Moduli Space
Sean Lawton, George Mason University
For other talks/presentations, check our departmental Colloquium and Seminars.