Department of Mathematics, Duke University

• Monday, September 27, 2021, 3:15pm, Physics 119, Geometry and Topology Seminar
  Solitons in Bryant’s Laplacian flow
  Mark Haskins (Duke University, Mathematics)

   

  The geometry of 3-forms in dimension 7 is very special, because of the existence of stable 3-forms, i.e. 3-forms whose orbit under GL(7) is an open subset of the space of all 3-forms. Such stable 3-forms turn out to be intimately related to the exceptional Lie group G_2, to the octonions and to so-called exceptional holonomy metrics, that is, Riemannian metrics whose holonomy group is contained in the group G_2. I will describe a geometric flow on closed 3-forms, due to Robert Bryant, called Laplacian flow that aims to produce Riemannian manifolds with holonomy group G_2. My talk will concentrate on certain special solutions to Laplacian flow called solitons: in particular I will describe recent constructions of non-compact shrinking, steady and expanding solitons in Laplacian flow. In other better-understood geometric flows, e.g. Ricci flow and mean curvature flow, solitons have played a key role in understanding singularity formation and hence in understanding the long-time behaviour of these flows. Time permitting I will make some comparisons with known solitons in Ricci flow and Lagrangian mean curvature flow. This is joint work with Johannes Nordström and also in part with Rowan Juneman (both at Bath).

• Wednesday, September 29, 2021, 3:15pm, Physics 119, Number Theory Seminar
  Self-dual cuspidal representations
  Manish Mishra (Indian Institute of Science Education and Research (IISER), Pune)

   

  Let F be a non-archimedean local field (such as ℚ_p). The Langlands philosophy says that the arithmetic of F is intimately related to the category R(G) of smooth complex representations of G(F) where G denotes a reductive F-group (for example the general linear group). The building blocks of R(G) are the "supercuspidal" representations of G(F). I will define this term in the talk. The category R(G) comes equipped with an involution - the "contragradient" or the "dual". The supercuspidal representations of G(F) which are self-dual are of considerable interest in the subject. In this talk, I will talk about a joint work with Jeff Adler about the existence of supercuspidals and self-dual supercuspidals. Specifically, we show that G(F) always admits supercuspidal representations. Under some mild hypotheses on G, we determine precisely when G(F) admits self-dual supercuspidal representations. These results are obtained from analogous results for finite reductive groups which I will also talk about.

• Thursday, September 30, 2021, 3:15pm, Virtual, Probability Seminar
  Can one prove existence of an infectiousness threshold (for a pandemic) in very general models of disease spread?
  David Aldous (UC Berkeley, Statistics)

   

  Intuitively, in any kind of disease transmission model with an infectiousness parameter, there should exist a critical value of the parameter separating a very likely from a very unlikely resulting pandemic. But even formulating a general conjecture is challenging. In the most simplistic model (SI) of transmission, one can prove this for an essentially arbitrary large weighted contact network. The proof for SI depends on a simple lemma concerning hitting times for increasing set-valued Markov processes. Can one extend to SIR or SIS models over similarly general networks, where the lemma is no longer applicable?

• Friday, October 1, 2021, 12:00pm, Physics 119, Mathematical Biology Seminar
  TBA
  Katie Newhall (University of North Carolina at Chapel Hill, Mathematics)

• Friday, October 1, 2021, 3:15pm, Virtual, Algebraic Geometry Seminar
  TBA by Leo Alonso Tarrio
  Leo Alonso Tarrio

• Wednesday, October 6, 2021, 3:15pm, Zoom link, Number Theory Seminar
  Number Theory Seminar
  Edna Jones

   

  TBD

• Thursday, October 7, 2021, 3:15pm, Virtual, Probability Seminar
  TBA
  Ahmed El Alaoui (Cornell University, Statistics and Data Science)

   

  abstract

• Friday, October 8, 2021, 12:00pm, Zoom, Mathematical Biology Seminar
  Mathematical models of cancer drug resistance
  Avner Friedman (The Ohio State University, Mathematics)

   

  Drug resistance is a primary obstacle in cancer treatment. In many patients who first respond well to treatment, relapse occurs within months. The question how to overcome drug resistance is currently explored in many clinical trials, by using combination of drugs, or by changing protocols of treatment. Mathematical model can be useful in explaining how resistance to cancer drug develops, and then suggesting how to overcome it with In this talk I will give several such examples. The mathematical models are represented by dynamical systems of PDEs for variables which are cells densities, concentrations of proteins (cytokines) and drugs, within a tumor; the tumor boundary is evolving in time, it is a free boundary, unknown in advance. The model is validated by comparison the simulations of the model with mice data. The drugs we shall consider are mostly immunotherapy, PD-1 and CTLA-4 inhibitors; these drugs, which were developed a few years ago, revolutionized the treatment of melanoma , lung cancer and other cancers, but have been associated with resistance.

• Monday, October 11, 2021, 3:15pm, Physics 119, Geometry/topology Seminar
  TBA
  Anthony Conway (MIT, Mathematics)

• Wednesday, October 13, 2021, 3:15pm, Physics 119, Number Theory Seminar
  TBA
  Rahul Dalal (JHU, Mathematics)

• Thursday, October 14, 2021, 3:15pm, Virtual, Probability Seminar
  title
  Ngoc Mai Tran (University of Texas at Austin, Mathematics)

   

  abstract

• Friday, October 15, 2021, 12:00pm, Zoom, Mathematical Biology Seminar
  TBA
  Nilima Nigam (Simon Fraser University, Mathematics)

• Monday, October 18, 2021, 3:15pm, Virtual, Geometry/topology Seminar
  TBA by Charanya Ravi
  Charanya Ravi (University of Regensburg, Mathematics)

• Wednesday, October 20, 2021, 3:15pm, Physics 119, Number Theory Seminar
  TBA
  Omer Offen (Brandeis, Mathematics)

• Thursday, October 21, 2021, 3:15pm, Virtual, Probability Seminar
  title
  Pratima Hebbar (Duke University, Mathematics)

   

  abstract

• Friday, October 22, 2021, 12:00pm, Zoom, Frontiers In Mathematics Seminar
  Frontiers
  Sarah Peluse (IAS/Princeton)

   

  TBA

• Monday, October 25, 2021, 3:15pm, Zoom link, Geometry/topology Seminar
  TBD
  Lucas Ambrozio (IMPA, Mathematics)

• Tuesday, October 26, 2021, 3:15pm, Zoom, Applied Math And Analysis Seminar
  TBA
  Daniel Eceizabarrena (University of Massachusetts Amherst)

   

  TBA

• Wednesday, October 27, 2021, 3:15pm, Physics 119, Number Theory Seminar
  TBA
  William Sokurski (Purdue, Mathematics)

• Thursday, October 28, 2021, 3:15pm, Virtual, Probability Seminar
  title
  Shirshendu Ganguly (UC Berkeley)

   

  abstract

• Friday, October 29, 2021, 12:00pm, Zoom, Frontiers In Mathematics Seminar
  Frontiers
  Sarah Peluse (IAS/Princeton)

   

  TBA

• Monday, November 1, 2021, 12:00pm, Zoom, Colloquium Seminar
  Colloquium
  Talea Mayo (Emory University)

   

  TBA

• Monday, November 1, 2021, 3:15pm, Physics 119, Geometry/topology Seminar
  TBA
  Miriam Kuzbary (Georgia Tech, Mathematics)

• Tuesday, November 2, 2021, 3:15pm, Virtual, Applied Math And Analysis Seminar
  TBA
  Haizhao Yang (Purdue, Mathematics)

   

  TBA

• Wednesday, November 3, 2021, 3:15pm, Physics 119, Number Theory Seminar
  TBA
  Zhilin Luo (University of Minnesota, Mathematics)

• Thursday, November 4, 2021, 3:15pm, Virtual, Probability Seminar
  title
  Daniel Lacker (Columbia University)

   

  abstract

• Friday, November 5, 2021, 12:00pm, Physics 119, Mathematical Biology Seminar
  TBA
  John Gemmer (Wake Forest University, Mathematics)

• Friday, November 5, 2021, 3:15pm, Physics 119, Number Theory Seminar
  tba
  David Schwein (University of Cambridge)

   

  tba

• Monday, November 8, 2021, 12:15pm, Zoom link, Frontiers In Mathematics Seminar
  Frontiers
  Marissa Kawehi Loving (Georgia Tech)

   

  TBA

• Monday, November 8, 2021, 3:15pm, Zoom link, Geometry & Topology Seminar
  TBA
  Weimin Chen (University of Massachusetts, Mathematics)

• Wednesday, November 10, 2021, 3:15pm, Physics 119, Number Theory Seminar
  TBA
  Jonathan P. Wang (Perimeter Institute, Mathematics)

• Monday, November 15, 2021, 12:15pm, Zoom link, Frontiers In Mathematics Seminar
  Frontiers
  Marissa Kawehi Loving (Georgia Tech)

   

  TBA

• Monday, November 15, 2021, 3:15pm, Virtual, Geometry & Topology Seminar
  TBA
  Honghao Gao (Michigan State University, Mathematics)

• Tuesday, November 16, 2021, 3:15pm, Zoom link, Applied Math And Analysis Seminar
  TBA
  Igor Kukavica (USC)

• Wednesday, November 17, 2021, 3:15pm, Physics 119, Number Theory Seminar
  TBA
  Jingwei Xiao (Princeton University, Mathematics)

• Friday, November 19, 2021, 12:00pm, Physics 119, Mathematical Biology Seminar
  TBA
  Kevin Flores (North Carolina State University, Mathematics)

• Monday, November 22, 2021, 3:15pm, Zoom link, Geometry/topology Seminar
  TBD
  Curtis Porter (Duke University, Mathematics)

• Monday, November 29, 2021, 3:15pm, Zoom link, Geometry/topology Seminar
  Tbd
  Raquel Perales (IMATE-UNAM, Mathematics)

   

  tbd

• Wednesday, December 1, 2021, 3:15pm, Physics 119, Number Theory Seminar
  TBA
  Melissa Emory (University of Toronto, Mathematics)

• Thursday, December 2, 2021, 3:15pm, Virtual, Probability Seminar
  title
  Roman Vershynin (University of California, Irvine, Mathematics)

   

  abstract