Seminar
Polarizations of Powers of Maximal Ideals in a Polynomial Ring
Abstract:
We give a complete combinatorial characterization of all possible polarizations of powers of the maximal ideal $(x_1,x_2,\dotsc,x_n)$ in a polynomial ring of $n$ variables. We also give a combinatorial description of the Alexander duals of such polarizations. In the three variable case we show that every polarization defines a (shellable) simplicial ball. We conjecture that any polarization of an artinian monomial ideal defines a simplicial ball. This is joint work with Gunnar Fløystad.
Uniform Large Deviations Principles
Abstract:
Triangulations of 3-manifolds through examples
Keller's Conjecture
Abstract:
Local existence of strong solution for the Cauchy problem of fully compressible Navier-Stokes equations in two dimensions
Large deviations for a class of semilinear stochastic partial differential equations in any space dimension
Abstract:
We prove the large deviation principle for the law of the solutions to a class of parabolic semilinear stochastic partial differential equations driven by multiplicative noise, in C[0,T] : Lρ(D) where D ⊂ Rd with d 1 is a bounded convex domain with smooth boundary and ρ is any real, positive and large enough number. The equation has nonlinearities of polynomial growth of any order, the space variable is of any dimension, and the proof is based on the weak convergence method.
“Generalized Fractional Integration.”
“Generalizing the Logistic Map. 3.”
Prime numbers and the Riemann zeta function
How are the prime numbers distributed among the integers? This question has been one of the greatest motivations to study math for multiple millennia. We'll try to tap in to some of this excitement, and also introduce some relations with the Riemann zeta function.