Department of

# Mathematics

Seminar Calendar
for events the day of Friday, February 12, 2021.

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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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Friday, February 12, 2021

2:00 pm in Contact for zoom link,Friday, February 12, 2021

#### The Largest Sum-free Subsets of Integers and its Generalization

###### Shukun Wu (UIUC Math)

Abstract: An old conjecture in additive combinatorics asks: what is the largest sum-free subset of any set of N positive integers? Here the word "largest" should be understood in terms of cardinality. For example, the largest sum-free subset of the first N positive integers has cardinality [(N+1)/2], which is the number of odd integers smaller than N, as well as the number of integers that lie in the interval [N/2,N]. In this talk, I will discuss a special case of the sum-free conjecture and the analogous conjecture on (k,l)-sum-free sets. This is a joint work with Yifan Jing

4:00 pm in Zoom,Friday, February 12, 2021

#### Geometry of Knots

###### Brannon Basilio (UIUC)

Abstract: In this talk, we give an introduction to the geometry of knots. We first start with an example of how to decompose a knot complement into ideal tetrahedron and the conditions needed in order to obtain a hyperbolic structure on the tetrahedron. We then talk briefly of recent work in knot theory that uses this decomposition to obtain bounds on the hyperbolic volume of the knot complement. For Zoom information, please email basilio3 (at) illinois (dot) edu.