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Wednesday, April 21st
10:25 AM

Self-Dual Bases for Self-Dual Hopf Algebras

Patrick Borse '21, Illinois Mathematics and Science Academy

10:25 AM - 10:40 AM

We consider when a graded, self-dual Hopf algebra A = A ,

with graded isomorphisms Φn: An → An* , has a self-dual basis. Motivated by the example of SSym over the reals, a self-dual algebra with no self-dual basis, we do this by analyzing the qualities of the map Φn. In particular, we have the general result that if ... Read More

10:45 AM

Hopf Algebra of k-Schur Functions and its Self-Duality

Rajan Patkar '21, Illinois Mathematics and Science Academy

10:45 AM - 11:05 AM

The k-Schur functions can be defined using several different methods, including using k-tableaux, weak tableaux, and strong tableaux (Lam et. al. 2013). They can be generated by a function derived from the weak Pieri rule for Schur functions, by summing over k-bounded partitions. These k-Schur functions also reside in a subring of the symmetric functions. The dual k-Schur functions can ... Read More

11:25 AM

Counting the Generalized and Extended Symmetric Spaces of SO(3,Fq)

Raman Aliakseyeu '21, Illinois Mathematics and Science Academy
Nat Oliven '21, Illinois Mathematics and Science Academy
Ethan Thieme '21, Illinois Mathematics and Science Academy

11:25 AM - 11:50 AM

In this paper we will provide a count for the size of both the generalized and extended symmetric spaces of SO(3,Fq) for all involutions when the characteristic is not equal to two. In addition we will explicitly describe the elements in the extended symmetric space and the fixed point group for both involutions.

11:55 AM

An Application of Compartmental Disease Modelling

Madhav Parthasarathy '21, Illinois Mathematics and Science Academy
Aidan Stueck '21, Illinois Mathematics and Science Academy

11:55 AM - 12:20 PM

As the coronavirus continues to plague the world, researchers are constantly working to model the spread of the disease and determine optimal means of containing the pandemic. Using a compartmental framework, we created a transition model that, by using available resources and ongoing research, was tailored to the COVID-19 pathogen. We classified the US population into different age groups and ... Read More