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for events the day of Friday, October 30, 2015.

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Friday, October 30, 2015

2:00 pm in 447 Altgeld Hall,Friday, October 30, 2015

Expandability of Discrete Analytic Functions

Fernando Roman-Garcia (UIUC Math)

Abstract: The class of discrete analytic functions is the discrete counterpart of the classical complex analytic functions. A noticeable peculiarity of discrete complex analysis is that the point-wise product of discrete analytic functions is not discrete analytic in general; for example, on the integer lattice in the complex plane, the functions z and z^2 are discrete analytic, but the function z^3 is not. Thus it is not an easy task to describe even the simplest algebraic discrete analytic functions, such as polynomials, rational functions or, even less, power series. Here we develop a basis of discrete analytic polynomials that allows power series expansion of discrete analytic functions.

2:00 pm in 143 Altgeld Hall,Friday, October 30, 2015

Remarks on the classification of semi-toric systems

Daniele Sepe   [email] (Universidade Federal Fluminense)

Abstract: Semi-toric systems are completely integrable Hamiltonian systems on four dimensional symplectic manifolds characterised by the existence of a global Hamiltonian circle action and by the restriction on their singular fibres, which, loosely speaking, are either of the type that appear in the toric case or an analogue of nodal singularities of Lefschetz fibrations. Intuitively speaking, on the one hand, the rigidity coming from the circle action allows one to classify these systems (a result due to Pelayo and Vu Ngoc), while the presence of nodes makes the classification sufficiently richer than that of (closed) symplectic toric manifolds. The aim of this talk is to provide a different point of view on the classification semi-toric systems, trying to interpret the invariants constructed by Pelayo and Vu Ngoc as describing a singular integral affine structure. These (simple!) remarks have arisen from independent conversations with Rui Loja Fernandes, Eugene Lerman, Silvia Sabatini and Susan Tolman.

4:00 pm in 243 Altgeld Hall,Friday, October 30, 2015

Homology of no k-equal manifolds

Nick Kosar (UIUC Math)

Abstract: No k-equal manifolds are generalizations of configuration spaces where we allow up to k-1 coordinates to be equal. Using a problem from computer science as motivation, I will talk about the homology of no k-equal manifolds of Euclidean space.

4:00 pm in 245 Altgeld Hall,Friday, October 30, 2015

Lecture 3. Webs, invariants, and clusters

Sergey Fomin (Robert M. Thrall Collegiate Professor of Mathematics, University of Michigan)

Abstract: Let V be a 3-dimensional complex vector space endowed with a volume form. The special linear group SL(V) naturally acts on collections of vectors, covectors, and matrices. A powerful tool for constructing and manipulating polynomial invariants of such actions is provided by the combinatorial machinery of tensor diagrams, which includes Kuperberg's diagrammatic calculus of webs. We use these techniques to describe and study cluster structures on classical rings of SL(V)-invariants. Based on joint work with D. Grigoriev, G. Koshevoy, P. Pylyavskyy, M. Shapiro, D. Thurston, and A. Zelevinsky.

4:00 pm in 345 Altgeld Hall,Friday, October 30, 2015

On "Surreal numbers, derivations and transseries" by A. Berarducci and V. Mantova [arXiv link]

Elliot Kaplan (UIUC Math)

Abstract: This talk will cover section 5 of the paper mentioned in the title on log-atomic numbers: a subclass of the surreals consisting of the infinite monomials which remain infinite monomials even after repeated iterations of the logarithm function. We will finish with a discussion of the $\kappa$-numbers, a subclass of the log-atomic numbers.