Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, November 20, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, November 20, 2014

10:00 am in 241 Altgeld Hall,Thursday, November 20, 2014

#### To Be Announced

Abstract: All talks will take place in 241 Altgeld Hall. Coffee and refreshments will be served in the common room, 321 AH, at 9:30 AM and 3:30 PM. Visit the U of I Langlands Day website http://www.math.illinois.edu/~mluu/conference.html for more information.

10:00 am in 143 Altgeld Hall,Thursday, November 20, 2014

#### The central limit theorem for dynamical systems

###### Byron Heersink (UIUC Math)

Abstract: In this talk, we outline the Nagaev-Guivarc'h method of extending the central limit theorem to certain dynamical systems using results from analytic perturbation theory.

11:00 am in 243 Altgeld Hall,Thursday, November 20, 2014

#### Goerss--Hopkins obstruction theory for $\infty$-categories

###### Aaron Mazel-Gee   [email] (UC Berkeley)

Abstract: Goerss--Hopkins obstruction theory is a tool for obtaining structured ring spectra from algebraic data. It was originally conceived as the main ingredient in the construction of tmf, although it's since become useful in a number of other settings, for instance in setting up a tractable theory of spectral algebraic geometry and in Rognes's Galois correspondence for commutative ring spectra. In this talk, I'll give some background, explain in broad strokes how the obstruction theory is built, and then indicate how one might go about generalizing it to an arbitrary (presentable) $\infty$-category. This last part relies on the notion of a model $\infty$-category -- that is, of an $\infty$-category equipped with a "model structure" -- which provides a theory of resolutions internal to $\infty$-categories and which will hopefully prove to be of independent interest.

1:00 pm in Altgeld Hall 243,Thursday, November 20, 2014

#### Long turns and the index of irreducible free group automorphisms

###### Martin Lustig (Université Aix-Marseille III)

Abstract: We will define the index of a free group automorphism \Phi as well as the index list of the corresponding outer automorphism \phi, and give a bit of a panorama. We will then explain how the index list of \phi can be computed from a train track representative of \phi. The main difficulty in a direct such calculation, so called INPs, can be controlled via studying "long turns", which is a new tool that has been invented and investigated in recent joint work with T. Coulbois. We will then present joint work with Coulbois and Pfaff which uses this tool crucially to show that any possible values for the index list can be achieved by some irreducible \phi. View talk at http://youtu.be/W3IVbxpzhkc

2:00 pm in 007 Illini Hall,Thursday, November 20, 2014

#### Jesmanowicz-Terai-Cao-Le Conjecture and Pure Ternary Exponential Diophantine Equations

###### Hui Lin Zhu (Xiamen University, China)

Abstract: In this talk we will introduce the Jesmanowicz-Terai-Cao-Le Conjecture and some results in pure ternary exponential Diophantine equations. We will discuss further research plan and ideas in this direction.

2:00 pm in 243 Altgeld Hall,Thursday, November 20, 2014

#### Noncommutative ergodic averages of balls and spheres, dimension free estimates

###### Guixiang Hong (Instituto de Ciencias Matematicas )

Abstract: In this talk, we would like to present some recent results on noncommutative ergodic theorems. Precisely, we establish the maximal ergodic theorem for the ergodic averages of balls and spheres in noncommutative $L_p$ spaces. As a consequence, we obtain noncommutative analogues of Wiener's and Jone's pointwise ergodic theorems. Moreover, using the noncommutative spherical maximal inequality, we prove that the bounds in the noncommutative Wiener's maximal inequalities are dimension free when the underlying von Neumann algebras are group measure spaces. If time is allowed, I will also present some results on the Heisenberg groups.

3:00 pm in 243 Altgeld Hall,Thursday, November 20, 2014

#### Associated Primes of Homologies arising from Approximation Theory

###### Michael DiPasquale (UIUC Math)

Abstract: Billera showed that the algebra of splines over a polytopal complex - of interest in approximation theory and geometric modelling - can be encoded as the top homology module of a certain chain complex. Schenck and Stillman introduced a variation of this chain complex whose homology modules are simpler. We show that the associated primes of the homology modules of this latter chain complex are all linear. This has consequences for computing the dimension of the vector space of splines of degree at most d on the underlying polytopal complex. In particular, we recover (in large degrees) a dimension formula for $C^1$ splines over a generic tetrahedral complex originally due to Alfeld, Schumaker, and Whiteley.

4:00 pm in 245 Altgeld Hall,Thursday, November 20, 2014

#### Maude-NPA: Cryptographic Protocol Analysis Modulo Equational Properties

###### Catherine Meadows (Naval Research Laboratory)

Abstract: Cryptographic protocols are the thread that knits together the security of the Internet. Thus it is important that they be correct. This is especially true for the design of the protocol. Although implementation errors are more common, design errors are harder to fix, especially for protocols, which must be both interoperable and widely deployed, making them difficult to redesign and redistribute on the fly. Indeed, even protocols with known flaws may remain deployed for a long time in order to support communication with legacy systems. For this reason, it is important to get a protocol right the first time. But since cryptographic protocols must be designed to operate in the face of an active attacker working to subvert their goals, this is not an easy problem.

One way of assuring correctness that has seen great success is the use of formal verification based on automated search techniques. One reason for this success has been the simple but powerful paradigm developed by Dolev and Yao in the late 70's and early 80's. In this paradigm messages are represented by symbolic terms constructed out of constants, function symbols, and variables. Furthermore, the network is controlled by an intruder who can intercept, destroy, and redirect traffic, and create and send messages of its own. Thus, we can think of the protocol as a distributed program for generating elements of a term algebra, defined by a set of rules that define actions executed by the intruder, and a set of rules describing actions executed by the honest principals.

Although the basic Dolev-Yao model is well-understood, it becomes more complex when we take into account the equational properties underlying the cryptoalgorithms used in the protocol, e.g. the axioms governing Abelian groups. However, it is necessary to do this, not only to faithfully represent the protocol, but in order to reason about the possible actions of an attacker. Thus, representation and reasoning about equational properties has been an active area of research. In this talk we will give an overview of research in this area, and present the approach used by a particular tool, the Maude-NRL Protocol Analyzer (Maude-NPA).