Events

In this talk, we consider exact identities for infinite sums of even divisor 
functions weighted by Laurent polynomials with logarithms for which the sum is 
absolutely convergent. Such identities are motivated by computations in string theory 
related to the scattering of 4-gravitons. We show that in general they give Fourier 
coefficients of holomorphic cusp forms using the method of holomorphic projection 
and discuss an application of spectral techniques to such sums. The talk is based on 

I will talk about Counting rational points on determinant surfaces $ad-bc =1$ using Analytic Number Theory approach. This problem is directly related to the shifted convolution sum of the restricted divisor function $\tau_X(n)$. Our method also allows us to restrict up to two of the entries to be primes.

Using finite dimensional Nichols algebras with automorphisms, we construct R-matrices with entries polynomials in the structure constants of the Nichols algebras. The R-matrices satisfy the Yang-Baxter equation and can be used to define multivariable polynomials of knots that generalize the colored Jones polynomial. For a Nichols algebra of rank 2, we define a sequence of polynomials $V_n(t,q)$ in two variables, whose first knot invariant is the Links-Gould polynomial and the second one $V_2$ is a new polynomial invariant that gives bounds for the Seifert-genus of a knot.