Department of

# Mathematics

Seminar Calendar
for events the day of Monday, October 12, 2015.

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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, October 12, 2015

4:00 pm in 141 Altgeld Hall,Monday, October 12, 2015

#### Forcing and Baire category: continued (the 3rd talk)

###### Anton Bernshteyn (UIUC Math)

Abstract: Forcing is a powerful tool invented by Paul Cohen for proving consistency and independence results. As we will see, forcing can be construed as a clever way to use Baire category. In this talk we will outline the method and its application to the independence of the Continuum Hypothesis from ZFC.

4:00 pm in 245 Altgeld Hall,Monday, October 12, 2015

#### A brief introduction to Brownian motion and Levy processes

###### Renming Song (Department of Mathematics, University of Illinois)

4:00 pm in 145 Altgeld Hall,Monday, October 12, 2015

#### Hyperplane Arrangement Complements - Topological Complexity and Zero-divisors-cup-length.

###### Nathan Fieldsteel (UIUC Math)

Abstract: The topological complexity $TC(X)$ of a space $X$ is an integer which measures the difficulty of finding a continuous motion planning algorithm for that space. While $TC(X)$ can be very difficult to compute in general, a lower bound can be obtained by computing the zero-divisors-cup-length of the cohomology of $X$, and this bound is conjectured to be sharp in many cases. One such case is when $X$ is the complement of a complex arrangement of hyperplanes. Such spaces have combinatorially determined cohomology rings called Orlik-Solomon algebras, and we will discuss progress towards finding a combinatorial formula for the zero-divisors-cup-length of these rings.

5:00 pm in 241 Altgeld Hall,Monday, October 12, 2015

#### Lp estimates on quantum channels

###### Gao Li (UIUC Math)

Abstract: Quantum channels are completely positive trace preserving (CPTP) maps. I will talk about some Lp norm estimates on "nice" classes of CPTP maps. This is a joint work with Marius Junge and Nicholas LaRacuente. The main tools we use are Haagerup tensor product, GNS construction and complex interpolation. If time permits, I will present some connections to quantum information theory.

5:45 pm in 241 Altgeld Hall,Monday, October 12, 2015