Department of

Mathematics


Seminar Calendar
for events the day of Thursday, February 28, 2019.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, February 28, 2019

11:00 am in 241 Altgeld Hall,Thursday, February 28, 2019

Using q-analogues to transform singularities

Kenneth Stolarsky (Illinois Math)

Abstract: This is a mostly elementary talk about polynomials and their q-analogues, filled with conjectures based on numerical evidence. For example, if ( x - 1 ) ^ 4 is replaced by a q-analogue, what happens to the root at x = 1 ? These investigations accidentally answer a question posed by J. Browkin about products of roots that was also answered by Schinzel some decades ago. We also look at how certain q-analogues are related to each other.

4:00 pm in 245 Altgeld Hall,Thursday, February 28, 2019

Quivers, representation theory and geometry

Kevin McGerty (University of Oxford and Visiting Fisher Professor, University of Illinois)

Abstract: A quiver is an oriented graph. It has a natural algebra associated to it called the path algebra, which as the name suggests has a basis given by paths in the quiver with multiplication given by concatenation. The representation theory of these algebras encompasses a number of classical problems in linear algebra, for example subspace arrangements and Jordan canonical form. A remarkable discovery of Gabriel however in the 1970s revealed a deep connection between these algebras and Lie theory, which has subsequently lead to a rich interaction between quivers, Lie theory and algebraic geometry. This talk will begin by outlining the elementary theory of representations of path algebras, explain Gabriel's result and survey some of the wonderful results which it has led to in Lie theory: the discovery of the canonical bases of quantum groups, the geometric realization of representations of affine quantum groups by Nakajima, and most recently deep connections between representations of symplectic reflection algebras and affine Lie algebras.