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Climate networks defined on a regular grid of geographic locations (nodes) covering the Earth's surface, built from the analysis of statistical interdependencies of climate time series, can provide useful information on large-scale patterns of climate variability. In this talk, I will discuss climate networks constructed from surface air temperature time series, using different methods such as Hilbert analysis, mutual information and Granger causality.

The research aimed at wind-wave interaction study in a big range of wind speeds, from light and moderate at a regional scale up to high wind speeds at hurricane wind conditions is performed. The regional model based on the WAVEWATCH III spectral wave model is adapted to the conditions of an inland water body using the WRF atmospheric model. Adaptation and verification of the models was carried out on the basis of the results of a series of field experiments to study the wind-wave regime of the Gorky reservoir performed in 2012–2019 using an autonomous buoy station based on the Froude oceanographic buoy. Within the framework of the WAVEWATCH III model, an analysis of the influence on the simulation result and subsequent adjustment of the parameters of the WAM 3 wind input parameterization was made, as well as the scheme for the approximate calculation of the Boltzmann integral Discrete Interaction Approximation (DIA) is adapted. Within the framework of the WRF model, calculations were c...

We will discuss ongoing work with Alexandra Florea, Matilde Lalín, and Amita Malik on the shifted convolution problem for divisor functions in function fields. This involves studying the average value of $d(f) d(f+h)$ where $h$ is a fixed polynomial (having possibly large degree $m$) in $\mathbb{F}_q[T]$ and $f$ runs over all monic polynomials in $\mathbb{F}_q[T]$ of degree $n$, where $n$ goes to infinity. Our techniques mirror the classical approach of Estermann in the integer setting. The main new ingredient is a functional equation for the Estermann function (equivalently, a Voronoi summation formula for the divisor function) that was not previously available in function fields. If time permits, we will discuss a related result involving the shifted convolution of the norm-counting functions of quadratic extensions. The talk should be accessible to those unfamiliar with function fields.

The second and fourth moments of the Riemann zeta function have been known for about a century, but the sixth moment remains elusive. The sixth moment of zeta can be thought of as the second moment of a GL_3 Eisenstein series, and it is natural to consider variants of the problem where the Eisenstein series is replaced by a cusp form. I will discuss recent work with Agniva Dasgupta and Wing Hong Leung where we obtain a nontrivial bound on this second moment. I will also discuss some applications, including an improvement on the Rankin-Selberg problem.

We explore approaches to systems of forms with differing degrees which use the ‘repulsion’ technique. This would allow for example asymptotic formulas for the density of solutions to nonsingular systems of Diophantine inequalities in sufficiently many variables.

We explore approaches to systems of forms with differing degrees which use the ‘repulsion’ technique. This would allow for example asymptotic formulas for the density of solutions to nonsingular systems of Diophantine inequalities in sufficiently many variables.

I will discuss the problem of obtaining an asymptotic formula for counting integral solutions to an equation of the form f(x, y, z, w)=N in an expanding box, where N is a non-zero integer and f is an indefinite quadratic form over the integers. For forms of the shape axy-bzw, I will then explain how we can obtain a significantly strong error term by applying deep methods from the spectral theory of automorphic forms. This is a joint work with Rachita Guria.