Colloquia & Seminars

Spring 2022 Colloquia

Title: "Machine-learning for mathematics: case study of number fields and elliptic curves"

Abstract: "In this talk, we will consider whether a machine can be trained to recognize patterns in mathematics. As a case study, some basic invariants in number theory such as the class number of a real quadratic field and the rank of an elliptic curve will be tested through machine-learning tools. We will observe that machine-learning classifiers perform surprisingly well with high accuracy (> 0.97)."

When: 

Dr. Kyu-Hwan Lee
Professor
Department of Mathematics
University of Connecticut

Where: Pickard Hall, Room 110


Spring 2022 Seminars

Title: "A DGA Resolution on Trimmings of Pfaffian Ideals and Applications to Tor Algebras"

Abstract: Let $(R,\mathfrak{m},\Bbbk)$ be a regular local ring of dimension 3. Let $I$ be a Gorenstein ideal of $R$ of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric matrix of odd size such that $I$ is generated by the sub-maximal pfaffians of this matrix. Let $J$ be the ideal obtained by multiplying some of the pfaffian generators of $I$ by $\mathfrak{m}$; we say that $J$ is a trimming of $I$. In this talk we will discuss an explicit construction of a free resolution of $R/J$ with a DG algebra structure. This work builds upon a recent paper of Vandebogert. We use our DG algebra resolution to prove that recent conjectures of Christensen, Veliche and Weyman on ideals of class $\mathbf{G}$ hold true in our context and to address the realizability question for ideals of class $\mathbf{G}$. This work is joint with Luigi Ferraro.

When: 

Alexis Hardesty
Ph.D. candidate
Department of Mathematics & Statistics
Texas Tech University

Where: Pickard Hall, Room 311