Department of

# Mathematics

Seminar Calendar
for events the day of Monday, October 5, 2020.

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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 5, 2020

3:00 pm in zoom,Monday, October 5, 2020

#### Microlocal sheaves on pinwheels and Fukaya categories of rational homology balls

###### Dogancan Karabas (Northwestern)

Abstract: It is shown by Kashiwara and Schapira (1980s) that for every constructible sheaf on a smooth manifold, one can construct a closed conic Lagrangian subset of its cotangent bundle, called the microsupport of the sheaf. This eventually led to the equivalence of the category of constructible sheaves on a manifold and the Fukaya category of its cotangent bundle by the work of Nadler and Zaslow (2006), and Ganatra, Pardon, and Shende (2018) for partially wrapped Fukaya categories. One can try to generalise this and conjecture that Fukaya category of a Weinstein manifold can be given by constructible (microlocal) sheaves associated with its skeleton. In this talk, I will briefly explain these concepts and confirm the conjecture for a family of Weinstein manifolds which are certain quotients of A_n-Milnor fibres. I will outline the computation of their wrapped Fukaya categories and microlocal sheaves on their skeleta, called pinwheels.

4:00 pm in via Zoom,Monday, October 5, 2020

#### Complexity and the second-order terms of capacity-achieving codes

###### Hsin-Po Wang   [email] (UIUC Math)

Abstract: Polar coding [Arıkan 2009] is a new tool to construct error correcting codes. It has practical uses and achieves capacity. A research interest is to characterize polar codes’ asymptotic behavior in terms of error probability, code rate, and time complexity; and improve them further. In this talk, two approaches to improvements will be elaborated. The first approach replaces the polarizing kernel [[1,0], [1,1]] by large, random, dynamic matrices to lessen the error probability and raise the code rate. The resulting performance catches up that of random code, which is the optimal one, while preserving the complexity of the original polar code. The second approach prunes the polarization process to reduce its complexity while maintaining the capacity-achieving property of the unpruned version. The resulting complexity is O(loglog(block length)) per information bit, while the unpruned version has O(log(block length)). Combining the two approaches yields a record-breaking tradeoff among rate, error, and complexity, giving a further contribution to the fundamental questions of Shannon. Please see https://calendars.illinois.edu/detail/2232/33389217 for Zoom login details.

5:00 pm in Altgeld Hall,Monday, October 5, 2020

#### On Harlow finite dimensional black holes

###### Marius Junge & Yidong Chen

Abstract: We will talk about finite dimensional C*algebras and entropy https://illinois.zoom.us/j/87316015196?pwd=dU9XZE0rbVZQeWRyY2w2TklDR051dz09