Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.


Past events in this series

Fri, 09 Jun 2023

North meets South

Dr Thomas Karam (North Wing) and Dr Hamid Rahkooy (South Wing)

North Wing talk: Dr Thomas Karam
Title: Ranges control degree ranks of multivariate polynomials on finite prime fields.

Abstract: Let $p$ be a prime. It has been known since work of Green and Tao (2007) that if a polynomial $P:\mathbb{F}_p^n \mapsto \mathbb{F}_p$ with degree $2 \le d \le p-1$ is not approximately equidistributed, then it can be expressed as a function of a bounded number of polynomials each with degree at most $d-1$. Since then, this result has been refined in several directions. We will explain how this kind of statement may be used to deduce an analogue where both the assumption and the conclusion are strengthened: if for some $1 \le t < d$ the image $P(\mathbb{F}_p^n)$ does not contain the image of a non-constant one-variable polynomial with degree at most $t$, then we can obtain a decomposition of $P$ in terms of a bounded number of polynomials each with degree at most $\lfloor d/(t+1) \rfloor$. We will also discuss the case where we replace the image $P(\mathbb{F}_p^n)$ by for instance $P(\{0,1\}^n)$ in the assumption.


South Wing talk: Dr Hamid Rahkooy
Title: Toric Varieties in Biochemical Reaction Networks

Abstract: Toric varieties are interesting objects for algebraic geometers as they have many properties. On the other hand, toric varieties appear in many applications. In particular, dynamics of many biochemical reactions lead to toric varieties. In this talk we discuss how to test toricity algorithmically, using computational algebra methods, e.g., Gröbner bases and quantifier elimination. We show experiments on real world models of reaction networks and observe that many biochemical reactions have toric steady states. We discuss complexity bounds and how to improve computations in certain cases.

Mon, 12 Jun 2023

Departmental Colloquium

George Lusztig
(Massachusetts Institute of Technology)
Further Information

George Lusztig is the Abdun-Nur Professor of Mathematics. He joined the MIT mathematics faculty in 1978 following a professorship appointment at the University of Warwick, 1974-77. He was appointed Norbert Wiener Professor at MIT 1999-2009.

Lusztig graduated from the University of Bucharest in 1968, and received both the M.A. and Ph.D. from Princeton University in 1971 under the direction of Michael Atiyah and William Browder. Professor Lusztig works on geometric representation theory and algebraic groups. He has received numerous research distinctions, including the Berwick Prize of the London Mathematical Society (1977), the AMS Cole Prize in Algebra (1985), and the Brouwer Medal of the Dutch Mathematical Society (1999), and the AMS Leroy P. Steele Prize for Lifetime Achievement (2008), "for entirely reshaping representation theory, and in the process changing much of mathematics."

Professor Lusztig is a Fellow of the Royal Society (1983), Fellow of the American Academy of Arts & Sciences (1991), and Member of the National Academy of Sciences (1992). He was the recipient of the Shaw Prize (2014) and the Wolf Prize (2022).