Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, February 25, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2014          February 2014            March 2014
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1  2  3  4                      1                      1
5  6  7  8  9 10 11    2  3  4  5  6  7  8    2  3  4  5  6  7  8
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Tuesday, February 25, 2014

8:00 am in CSL,Tuesday, February 25, 2014

#### IMSE Hot TIME Symposium: Applied Geometry, Topology and Networks

Abstract: IMSE Hot TIME Symposium: Applied Geometry, Topology and Networks takes place on February 24-25 on campus, featuring Ruth Williams and Frank Sottile as plenary speakers and 20 invited talks by experts from 12 universities and LANL. The details are at https://imse.math.illinois.edu/?page_id=603 - the program is broad and interesting. Join us!

11:00 am in 243 Altgeld Hall,Tuesday, February 25, 2014

#### Operads, and their algebras, for building new processors from old

###### David Spivak (MIT)

Abstract: In this talk, I'll write down a very simple (colored) operad O that models information processing in a network, or material flow through a system. Basically, the morphisms of O look like boxes wired together inside a box; the outer box as a process is constituted by the wiring pattern of its constitutents. I'll discuss an O-algebra of state machines, as well as perhaps some monadic extensions. I'll also discuss a connection between the algebras on a wiring diagram operad and traced monoidal categories. This is joint work with Dylan Rupel and Nat Stapleton.

2:00 pm in 241 Altgeld Hall,Tuesday, February 25, 2014

#### Generic representations of Abelian groups and extreme amenability (part 2)

###### Anush Tserunyan (UIUC Math)

Abstract: We continue working through "Generic representations of Abelian groups and extreme amenability" by Melleray and Tsankov. We aim at showing that for an abelian group $\Gamma$ containing an element of infinite order, $\{\phi \in \text{Hom}(\Gamma, \text{Aut}(X,\mu)) : \overline{\phi(\Gamma)} \cong L^0(\mathbb{T})\}$ is dense, for which it is enough to show that there is one essentially free such $\phi \in \text{Hom}(\Gamma, \text{Aut}(X,\mu))$. The main ingredient of the construction is showing that $\{\phi \in \text{Hom}(\Gamma, L^0(\mathbb{T})) : \phi(\Gamma) \text{ dense in } L^0(T)\}$ is a dense $G_\delta$ set.

2:00 pm in Altgeld Hall 347,Tuesday, February 25, 2014

#### Correlation of Intracellular Components due to Limited Processing Resources

###### Ruth Williams (UCSD Math)

Abstract: A major challenge for systems biology is to deduce the molecular interactions that underlie correlations observed between concentrations of different intracellular components. Of particular interest is obtaining an understanding of such effects when biological pathways share common elements that are limited in capacity. Here we use stochastic models to explore the effect of limited processing resources on correlations when these resources are positioned downstream or upstream of the molecular species of interest. Specifically, we consider two situations where correlations in protein levels are the object of interest: (i) degradation of different proteins by a common protease, and (ii) translation of different mRNA transcripts by a limited pool of ribosomes. In developing and analyzing stochastic models for these systems, we use insights from the mathematical theory of multiclass queues which was originally developed to understand congestion effects in telecommunication, computer, manufacturing and business systems. In both models we observe a correlation resonance: correlations tend to have a peak slightly beyond the point where the systems transition from underloading to overloading of the processing resources, although the sign of the correlation is different in the two cases. As time permits, related experimental work will be described.

3:00 pm in 241 Altgeld Hall,Tuesday, February 25, 2014

#### Covering 2-edge-colored graphs with a pair of cycles

###### Louis DeBiasio   [email] (Miami University)

Abstract: Lehel conjectured that in every $2$-coloring of the edges of $K_n$, there is a vertex disjoint red and blue cycle which span $V(K_n)$. Łuczak, Rödl, and Szemerédi proved Lehel's conjecture for large n, Allen gave a different proof for large $n$, and finally Bessy and Thomassé gave a proof for all n. Balogh, Barát, Gerbner, Gyárfás and Sárközy conjectured a strengthening of Lehel's conjecture where $K_n$ is replaced by any graph G with minimum degree at least $3n/4$, and they proved an approximate version of their conjecture. We prove that their conjecture holds for sufficiently large $n$. (Joint work with Luke Nelsen)

3:00 pm in 243 Altgeld Hall,Tuesday, February 25, 2014

#### Morse Theory of D-Modules

###### Thomas Nevins (UIUC Math)

Abstract: Hamiltonian reduction arose as a mechanism for reducing complexity of systems in mechanics, but it also provides a tool for constructing complicated but interesting algebraic varieties from simpler ones. I will illustrate how this works via examples. I will explain a new structure theory, motivated by Hamiltonian reduction, for some categories (of D-modules) of interest to representation theorists, and, if there is time, indicate applications to the cohomology of (hyperkaehler) manifolds. The talk will not assume that members of the audience know the meaning of any of the above-mentioned terms. The talk is based on joint work with K. McGerty.

4:00 pm in Altgeld Hall,Tuesday, February 25, 2014

#### Implicitization Using Approximation Complexes

###### Eliana Duarte (UIUC Math)

Abstract: I will present the method of using approximation complexes to compute the image of a rational map from $\mathbb{P}^{n-1}$ to $\mathbb{P}^{n}$, under some hypotheses on the base locus and on the image. The method uses tools from commutative algebra such as Koszul complexes and Castelnuovo-Mumford regularity which I will introduce.