Department of

# Mathematics

Seminar Calendar
for events the day of Monday, April 14, 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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Monday, April 14, 2014

3:00 pm in 145 Altgeld Hall,Monday, April 14, 2014

#### Transverse Geometry of Codimension one Foliations Calibrated by Closed 2-Forms

###### David Martinez Torres (PUC-Rio de Janeiro)

Abstract: A codimension one foliation is (topologically) taut if it admits a closed 1-cycle everywhere transverse to the foliation. The theory of taut foliations is extremely rich in dimension 3, however, it less satisfactory in higher dimensions. In this talk we will discuss a different generalization of 3-dimensional taut foliati- ons to higher dimensions inspired in symplectic geometry. These are codimension one foliations which admit a closed 2-form which makes every leaf a symplectic manifold. Our main result is that on an ambient closed manifold a foliation (of class at least C^1 in the transverse direction) admitting a 2-calibration has its transverse geometry encoded in a 3-dimensional foliated submanifold. This is joint work with Álvaro del Pino and Francisco Presas (ICMAT, Madrid)

4:00 pm in 165 Everitt Lab,Monday, April 14, 2014

#### Wolfram|Alpha Pro and Mathematica 9

Abstract: During this free seminar, explore using Mathematica and Wolfram|Alpha Pro for a wide variety of practical and theoretical applications across a variety of disciplines. Attendees will not only see new features in Wolfram|Alpha Pro and Mathematica 9, but will also receive examples of this functionality to begin using immediately. No Mathematica experience is required, and students are encouraged to attend. Register at http://webstore.illinois.edu/wolfram

4:00 pm in 143 Altgeld Hall,Monday, April 14, 2014

#### The (2,2) sigma model and its topological twists

###### Sheldon Katz (Illinois Math)

Abstract: I begin by describing the sigma model with target a Kahler manifold X, a two-dimensional quantum field theory with (2,2) supersymmetry on a Riemann surface $\Sigma$. I then describe its topological twists, the A-model and the B-model. The A-model localizes on holomorphic maps $\phi:\Sigma\to X$ and its correlation functions are precisely the Gromov-Witten invariants if $\Sigma$ has genus 0. The B model localizes on constant maps, hence its correlation functions are given by integrals on X. Finally, I describe the setup of mirror symmetry, whereby enumerative invariants of curves on Calabi-Yau manifolds can be computed by classical integrals on a mirror Calabi-Yau manifold.

4:00 pm in 241 Altgeld Hall,Monday, April 14, 2014

#### Are branched expanding maps $f: S^2 \to S^2$ smoothable?

###### Kevin Pilgrim (Indiana)

Abstract: Branched expanding maps $f: S^2 \to S^2$ generalize piecewise expanding multimodal maps of the interval and are the object of much recent study (Cannon-Floyd-Parry; Haissinsky-P.; Bonk-Meyer; Meyer; Nekrashevych). Typically, these are presented only indirectly, and one does not have any good "normal forms" for topological conjugacy classes, e.g. smooth, piecewise affine, etc. models. Are these subsumed in the theory of smooth dynamics? This ignorance contrasts greatly with what we know about expanding maps of circles, intervals, and (infra nil) manifolds. I will focus on several different ways of constructing examples: matings (with movies), subdivision rules (with pictures), contracting virtual endomorphisms of orbifold fundamental groups (with algebra formulas) and other rare examples (with exact formulas).

5:00 pm in 241 Altgeld,Monday, April 14, 2014

#### On Junge's Problem

###### Ali Kavruk (UIUC Math)

Abstract: In quantum information, Peres–Horodecki criterion (positive partial transpose or PPT) is sufficient to determine separability of a quantum state when the underlying Hilbert space dimensions are low (2x2, 2x3, 3x2). Junge's problem states that, for any local dimension, bi-PPT quantum cones can be used to detect separability. In this talk we will focus on general theory of symmetrization in operator systems, and study their functorial properties. Then we will obtain some formulations of Junge's problem. We will also outline some connection with Tsirelson's problem in quantum information.