Department of

# Mathematics

Seminar Calendar
for events the day of Monday, November 11, 2019.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, November 11, 2019

3:00 pm in 441 Altgeld Hall,Monday, November 11, 2019

#### Introduction to Picard groups

###### Venkata Sai Narayana Bavisetty (UIUC Math)

Abstract: Picard groups have been classically studied in commutative algebra and algebraic geometry. These can be suitably generalised to define picard groups of $\mathbb{E}_{\infty}$ ring spectra. In this situation a natural question to ask is "How is the picard group of $R$ related to the picard group of $R_*$?". In this expository talk, I will explain some methods which have been used to answer the above question.

5:00 pm in 241 Altgeld Hall,Monday, November 11, 2019

#### CLSI of graphs

###### Nicholas LaRacuente (University of Illinois at Urbana-Champaign)

Abstract: Quantum Markov semigroups (QMSs) model continuous time-evolution of quantum states exposed to environmental noise. A key aspect of a selfadjoint QMS is how quickly an arbitrary state or density decays toward an invariant fixed point algebra. A modified logarithmic Sobolev inequality (MLSI) quantifies exponential decay of relative entropy with respect to the fixed point algebra. A complete logarithmic Sobolev inequality (CLSI) does so in the presence of an arbitrary auxiliary system that is untouched by decay. I will describe our recent proof that error models described by finite graphs have CLSI. This follows joint work with Marius Junge and Haojian Li.