Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, March 24, 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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Tuesday, March 24, 2020

11:00 am in 243 Altgeld Hall,Tuesday, March 24, 2020

#### CANCELLED

###### Christina Osborne (OSU Math)

1:00 pm in https://illinois.zoom.us/j/249415194,Tuesday, March 24, 2020

#### Borel structures on the space of left orderings

###### Filippo Calderoni (UIC Math)

Abstract: In this talk I will present some recent results on left-orderable groups and their interplay with descriptive set theory. We shall discuss how Borel classification can be used to analyze the space of left-orderings of a given countable group modulo the conjugacy action. In particular we shall see that if G is a countable nonabelian free group, then the conjugacy relation on its space of left orderings is a universal countable Borel equivalence relation. This is joint work with A. Clay.

2:00 pm in Altgeld Hall,Tuesday, March 24, 2020

#### with Felix Lediztky

###### Felix Lediztky (Waterloo)

Abstract: Felix will answer questions by students. https://illinois.zoom.us/j/618149894

4:00 pm in Zoom Meeting https://illinois.zoom.us/j/314999665,Tuesday, March 24, 2020

#### Error Thresholds for Arbitrary Pauli Noise

###### Felix Leditzky (Institute for Quantum Computing, University of Waterloo; and Perimeter Institute)

Abstract: The error threshold of a one-parameter family of quantum channels is defined as the largest noise level such that the quantum capacity of the channel remains positive, which in turn guarantees existence of quantum error correction codes. Here, we study the error thresholds of channels arising from probabilistic Pauli errors. To this end, we determine lower bounds on the quantum capacity of these channels by evaluating the coherent information of so-called graph states affected by Pauli noise. Graph states are a subclass of stabilizer states and uniquely defined by a simple undirected graph. The main tools for our results are a) a simplified analysis of the channel action on graph states using the language of homomorphic group actions, and b) using strong generating systems for permutation groups to implement the algorithm in a computationally efficient manner. We provide an extensive analysis of known good codes such as repetition codes and cat codes in the whole Pauli channel simplex. Furthermore, we identify a novel family of quantum codes based on tree graphs with desirable error correction properties. This meeting will be a Zoom meeting! To participate, go to https://illinois.zoom.us/j/314999665 (please watch out for changes)