Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, September 24, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2014           September 2014          October 2014
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1  2       1  2  3  4  5  6             1  2  3  4
3  4  5  6  7  8  9    7  8  9 10 11 12 13    5  6  7  8  9 10 11
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Wednesday, September 24, 2014

2:00 pm in 441 Altgeld Hall,Wednesday, September 24, 2014

#### Points in $\mathbb{P}^n$ Versus Points in Multiprojective Space

###### Eliana Duarte   [email] (UIUC Math)

Abstract: In this talk I will compare properties of sets of points in $\mathbb{P}^n$ to properties of sets of points in multiprojective space. We will review some concepts like Hilbert functions, primary decomposition and the Cohen-Macaulay property. Towards the end I will present a combinatorial characterization of arithmetically Cohen-Macaulay fat point schemes in $\mathbb{P}^1 \times \mathbb{P}^1$.

3:00 pm in 243 Altgeld Hall (Note different room than usual),Wednesday, September 24, 2014

#### Steep tilings and sequences of interlaced partitions

###### Jérémy Bouttier (Institut de Physique Théorique CEA, Saclay and École Normale Supérieure, Paris)

Abstract: We present a general bijection between a family of domino tilings (the so-called "steep tilings") and sequences of partitions where, at each step, one adds or removes an horizontal or vertical strip. As particular cases, we recover domino tilings of the Aztec diamond and pyramid partitions. We will discuss some applications concerning enumeration, asymptotic shapes and random generation. Based on joint work with Sylvie Corteel, Guillaume Chapuy and later on with Cédric Boutillier, Sanjay Ramassamy and Mirjana Vuletić.

4:00 pm in 245 Altgeld Hall,Wednesday, September 24, 2014

#### First Passage Percolation on Lattices

###### Partha Dey (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: First passage percolation is a simple model of random geometry on graphs. Given the d-dimensional euclidean lattice with i.i.d. nonnegative edge weights one considers the asymptotic behavior of large balls in the randomly weighted graph and geodesics or distance minimizing paths between two `far’ points. The boundary fluctuation of the large balls are conjectured to have a universal behavior for any fixed dimension. In this talk, we will discuss some aspects of standard and long-range first passage percolation, where one observes various phase transitions and connect them to the global universality picture.

4:30 pm in 243 Altgeld Hall,Wednesday, September 24, 2014

#### Area-1 Rectangulations

###### Richard Kenyon (Brown University)

Abstract: We show that the map from conductances to edge energies in a purely resistive circuit is surjective. As a consequence one can find, for any tiling of a rectangle with rectangles, a combinatorially equivalent tiling with prescribed rectangle areas. We also identify the degree of the above map with the number of acyclic orientations with one sink and one source, of the underlying graph. This number can also be identified with the x-derivative of the Tutte polynomial at (0,0).