1. K-State home
  2. »Division of Communications and Marketing
  3. »K-State Today
  4. »Mathematics Colloquium lecture today

K-State Today

March 27, 2014



Mathematics Colloquium lecture today

By Reta McDermott

Alexander Polishchuk, University of Oregon, will present "Analogs of the j-invariant for Higher Genus Curves" as part of the mathematics department Colloquium lecture series at 2:30 p.m. Thursday, March 27, in 102 Cardwell Hall.

The abstract for the lecture is: The j-invariant of an elliptic curve plays a central role in the classical theory of elliptic curves and modular functions. In the first part of the talk I will present an analogous construction for higher genus curves that uses only elementary algebraic geometry of curves. Then I will discuss how the j-invariant and its higher genus analogs appear in the study of certain A-infinity algebras associated with algebraic curves. A-infinity algebras are generalizations of usual algebras - in addition to double products they are equipped with n-tuple products satisfying appropriate higher associativity constraints. The homological mirror symmetry conjecture of Kontsevich relates some natural A-infinity algebras appearing in symplectic geometry with those appearing in algebraic geometry. The A-infinity algebras discussed in my talk are expected to appear on algebro-geometic side of this picture in the case of genus 1 the mirror symmetry equivalence has been established.

In this issue

From the administration
News and research
Shared governance
Events
Kudos, publications and presentations
Publications and presentations
Human resources, benefits and training
Campus construction and maintenance
Newsletters and magazines