Mathematics
2021  
Wednesday, April 21st  

10:25 AM 
SelfDual Bases for SelfDual Hopf Algebras Patrick Borse '21, Illinois Mathematics and Science Academy 10:25 AM  10:40 AM We consider when a graded, selfdual Hopf algebra A = A , with graded isomorphisms Φ_{n}: A_{n }→ A_{n}^{* }, has a selfdual basis. Motivated by the example of SSym over the reals, a selfdual algebra with no selfdual basis, we do this by analyzing the qualities of the map Φ_{n}. In particular, we have the general result that if ... Read More 

10:45 AM 
Hopf Algebra of kSchur Functions and its SelfDuality Rajan Patkar '21, Illinois Mathematics and Science Academy 10:45 AM  11:05 AM The kSchur functions can be defined using several different methods, including using ktableaux, 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 kbounded partitions. These kSchur functions also reside in a subring of the symmetric functions. The dual kSchur 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 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 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 COVID19 pathogen. We classified the US population into different age groups and ... Read More 