Date: | February 26, 2018 |

Time: | 2:00PM - 3:00PM |

Location: | BLOC 220 |

Speaker: | Erik Lundberg, Florida Atlantic University |

Title: | Random matrices arising in the study of random fields |

Abstract: | Certain problems in random fields, such as studying the solutions to a random system of equations (e.g., the critical points of a random potential energy landscape) have made important use of random matrix theory. After surveying some applications related to classical random matrix ensembles, we present a new direction in random fields concerning the solutions to problems in enumerative geometry (e.g., the number of lines on a random cubic surface). The resulting random matrices are of a special structured type. We conclude with some open problems that are simple to state. This is joint work with Saugata Basu, Antonio Lerario, and Chris Peterson. |

Date: | February 26, 2018 |

Time: | 3:00PM - 4:00PM |

Location: | BLOC 628 |

Speaker: | Ron Rosenthal, Technion |

Title: | Random Steiner complexes |

Abstract: | We will discuss a new model for random d-dimensional simplicial complexes, for d ≥ 2, whose (d − 1)-cells have bounded degrees. The construction relies on Keevash's results on the existence of Steiner systems which are generalizations of regular graphs. We will show that with high probability, complexes sampled according to this model are high-dimensional expanders. This gives a full solution to a question raised by Dotterrer and Kahle, which was solved in the two-dimensional case by Lubotzky and Meshulam. In addition, we will discuss the limits of their spectral measures and their relation to the spectral measure of certain high-dimensional regular trees. Based on a joint work with Alex Lubotzky and Zur Luria and a work in progress with Yuval Peled. |

Date: | February 26, 2018 |

Time: | 3:00PM - 3:50PM |

Location: | BLOC 506A |

Speaker: | Jintao Deng, Texas A&M University |

Title: | Groupoid II |

Date: | February 26, 2018 |

Time: | 5:00PM - 6:00PM |

Location: | BLOC 628 |

Speaker: | JM Landsberg, TAMU |

Title: | Strassen II |

Date: | February 28, 2018 |

Time: | 1:15PM - 2:15PM |

Location: | BLOC 220 |

Speaker: | Wei-Lun Tsai, Texas A&M University |

Title: | Analytic formulas for Stark units in quadratic extensions of totally real cubic fields |

Abstract: | In this talk, we will explain how Stark units in certain quadratic extensions of totally real cubic fields can be evaluated explicitly in terms of values of the Barnes triple Gamma function at algebraic arguments. This is joint work with Adrian Barquero-Sanchez and Riad Masri. |

Date: | February 28, 2018 |

Time: | 3:00PM - 4:00PM |

Location: | BLOC 628 |

Speaker: | Abner Salgado, University of Tennessee |

Title: | Finite element approximation of nonconvex uniformly elliptic fully nonlinear equations |

Abstract: | We propose and analyze a two-scale finite element method for the Isaacs equation. By showing the consistency of the approximation and that the method satisfies the discrete maximum principle we establish convergence to the viscosity solution. By properly choosing each of the scales, and using the recently derived discrete Alexandrov Bakelman Pucci estimate we can deduce rates of convergence. |

Date: | February 28, 2018 |

Time: | 6:00PM - 7:00PM |

Location: | BLOC 220 |

Speaker: | Dr. Andrew Bridy, Texas A&M University, Department of Mathematics |

Title: | Integer Factorization and Cryptography |

Abstract: | The security of modern cryptography largely depends on the fact that factoring integers is a computationally expensive problem (at least, until quantum computers become practical). We will discuss the difficulty of factoring, as well as some factoring algorithms that are significantly faster than the naive "trial division" method. |

Date: | March 2, 2018 |

Time: | 3:00PM - 4:00PM |

Location: | BLOC 628 |

Speaker: | Shilin Yu, Texas A&M University |

Title: | TBA |

Date: | March 2, 2018 |

Time: | 4:00PM - 5:00PM |

Location: | BLOC 628 |

Speaker: | J. Weyman, U. Conn. |

Title: | TBA |

Date: | March 5, 2018 |

Time: | 3:00PM - 3:50PM |

Location: | BLOC 628 |

Speaker: | Frank Sottile, Texas A&M University |

Title: | Intersection Theory in Numerical Algebraic Geometry |

Abstract: | I will describe how some ideas from intersection theory are useful in numerical algebraic geometry. The fundamental data structure in numerical algebraic geometry is that of a witness set, which is considered to be an instantiation of Weil’s notion of a generic point. Reinterpreting a witness set in terms of duality of the intersection pairing in intersection theory leads to a generalization of the notion that makes sense on many spaces and leads to a general notion of a witness set. I will also describe how rational equivalence is linked to homotopy methods. These notions are most productive for homogenous spaces, such as projective spaces, Grassmannians, and their products. After explaining the general theory, I will sketch what this means for the Grassmannian. This is joint work with Bates, Hauenstein, and Leykin. |

Date: | March 5, 2018 |

Time: | 5:00PM - 6:00PM |

Location: | BLOC 628 |

Speaker: | K. Bari, TAMU |

Title: | The hay in a haystack problem |

Date: | March 7, 2018 |

Time: | 6:00PM - 7:00PM |

Location: | BLOC 220 |

Speaker: | Dr. Sinjini Sengupta, Texas A&M University, Department of Mathematics |

Title: | TBA |

Date: | March 8, 2018 |

Time: | 4:00PM - 5:00PM |

Location: | BLOC 220 |

Speaker: | Nordine Mir, Texas A&M University - Qatar |

Title: | TBA |

Abstract: | TBA |

Date: | March 9, 2018 |

Time: | 1:50PM - 2:50PM |

Location: | BLOC 628 |

Speaker: | Peter Kuchment, Texas A&M |

Title: | On Liouville-Riemann-Roch theorems on co-compact abelian coverings |

Abstract: | A generalization by Gromov and Shubin [2-3] of the classical Riemann-Roch theorem describes the index of an elliptic operator on a compact manifold with a divisor of prescribed zeros and allowed singularities. On the other hand, Liouville type theorems count the number of solutions of a given polynomial growth of the Laplace-Beltrami (or more general elliptic) equation on a non-compact manifold. The solution of a 1975 Yau's conjecture [6] by Colding and Minicozzi [1] implies in particular, that such dimensions are finite for Laplace-Beltrami equation on a nilpotent co-compact covering. In the case of an abelian covering, much more complete Liouville theorems (including exact formulas for dimensions) have been obtained by Kuchment and Pinchover [4-5]. One wonders whether such results have a combined generalization that would allow for a divisor that "includes the infinity." Surprisingly, combining the two types of results turns out being rather non-trivial. The talk will present such a result obtained recently in a joint work with Minh Kha (former A&M PhD student, currently postdoc at U. Arizona). [1] Colding, T. H., Minicozzi, W. P.: Harmonic functions on manifolds, Ann. of Math. 146 (1997), 725–747. [2] M. Gromov and M. A. Shubin, The Riemann-Roch theorem for elliptic operators, I. M. Gel'fand Seminar, 1993, pp. 211--241. [3] --" -- , The Riemann-Roch theorem for elliptic operators and solvability of elliptic equations with additional conditions on compact subsets, Invent. Math. 117 (1994), no. 1, 165--180. [4] P. Kuchment and Y. Pinchover, Integral representations and Liouville theorems for solutions of periodic elliptic equations, J. Funct. Anal. 181 (2001), no. 2, 402--446. [5] --"-- , Liouville theorems and spectral edge behavior on abelian coverings of compact manifolds, Trans. Amer. Math. Soc. 359 (2007), no. 12, 5777--5815. [6] Yau, S. T.: Harmonic functions on complete Riemannian manifolds, Commun. Pure Appl. Math. 28 (1975), 201–228. |

Date: | March 9, 2018 |

Time: | 4:00PM - 5:00PM |

Location: | BLOC 220 |

Speaker: | Alexandru Chirvasitu, University at Buffalo |

Title: | TBA |

Date: | March 19, 2018 |

Time: | 3:00PM - 4:00PM |

Location: | BLOC 628 |

Speaker: | F. Gesmundo, U. Copenhagen |

Title: | TBA |

Date: | March 19, 2018 |

Time: | 4:00PM - 5:00PM |

Location: | Blocker 117 |

Speaker: | Yakov Sinai, Princeton University |

Title: | TBA |

Date: | March 19, 2018 |

Time: | 5:00PM - 6:00PM |

Location: | BLOC 628 |

Speaker: | F. Gesmundo |

Title: | Details |

Date: | March 20, 2018 |

Time: | 4:00PM - 5:00PM |

Location: | Blocker 117 |

Speaker: | Yakov Sinai, Princeton University |

Title: | TBA |

Date: | March 21, 2018 |

Time: | 6:00PM - 7:00PM |

Location: | BLOC 22 |

Speaker: | Dr. Frank Sottile, Texas A&M University, Department of Mathematics |

Title: | Some Algebraic Geometry in Applications |

Abstract: | Algebraic geometry is the study of sets which arise as the common zeroes to a collection of polynomials. It is a deep and powerful subject, combining geometric intuition with algebraic precision. It is also increasingly a useful tool in applications of mathematics, for whenever polynomials arise, the methods of algebraic geometry may be brought to bear on the problem at hand. I will illustrate this growing trend through a series of interrelated examples of algebraic geometry arising in applications. |

Date: | March 22, 2018 |

Time: | 4:00PM - 5:00PM |

Location: | Blocker 117 |

Speaker: | Yakov Sinai, Princeton University |

Title: | TBA |

Date: | March 23, 2018 |

Time: | 3:00PM - 3:50PM |

Location: | BLOC 628 |

Speaker: | Dimitar Grantcharov, UT Arlington |

Title: | TBA |