Events for 03/25/2019 from all calendars
Geometry Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 628
Speaker: E. Ventura, TAMU
Title: Tensors and their symmetry groups
Abstract: Tensors (multi-dimensional matrices) appear in many areas of pure and applied mathematics. I will discuss their use in algebraic complexity theory. Matrix multiplication is a tensor and its complexity is encoded in its tensor rank. To analyze the complexity of the matrix multiplication tensor, Strassen introduced a class of tensors that vastly generalize it, the tight tensors. These tensors have continuous symmetries. Pushing Strassen’s ideas forward, with A. Conner, F. Gesmundo, and J.M. Landsberg, we investigate tensors with large symmetry groups and classify them under a natural genericity assumption. Our study provides new paths towards upper bounds on the complexity of matrix multiplication.
Industrial and Applied Math
Time: 4:00PM - 5:00PM
Location: BLOC 220
Speaker: Carsten Conradi, HTW Berlin
Title: Establishing multistationarity conditions for polynomial ODEs in biology
Abstract: Polynomial Ordinary Differential Equations are an important tool in many areas of quantitative biology. Due to large measurement uncertainty, few experimental repetitions and a limited number of measurable components, parameter values are accompanied by large confidence intervals. One therefore effectively has to study families of parametrized polynomial ODEs. Multistationarity, that is the existence of at least two positive solutions to the steady state equations has been recognized as an important qualitative property of these ODEs. As a consequence of parameter uncertainty numerical analysis often fails to establish multistationarity. Hence techniques allowing the analytic computation of parameter values where a given system exhibits multistationarity are desirable. In my talk I focus on ODEs that are dissipative and where additionally the steady state variety admits a monomial parameterization. For such systems multistationarity can be decided by studying the sign of the determinant of the Jacobian evaluated at this parameterization. I present examples where this allows to determine semi-algebraic descriptions of parameter regions for multistationarity.