Mathematics

Title: Gamma-factor for representations of covering groups in the spirit of the Langlands-Shahidi method.

Abstract: The Langlands-Shahidi method associates a gamma-factor to representations of quasi-split reductive groups defined over local fields, exploiting the uniqueness of the Whittaker model. In our talk we shall give a speculative definition for a gamma-factor in the context of covering groups in the spirit of this method although the uniqueness of the Whittaker model fails. We shall...

Title: Fibonacci and related numbers in determinants

Abstract: There are many references to matrices or determinants that have Fibonacci numbers as elements. In this talk, we show several determinants expressing the Fibonacci and related polynomials. This method is well-applicable to other numbers or polynomials too. In addition, these results, based on the form of the Hessenberg matrix, allow for many applications such as inverse formulas, explicit expressions, and continued fraction...

Title: Finding needles in haystacks: Boolean intervals in the weak order of $\mathfrak{S}_n$

Abstract: Finding and enumerating Boolean intervals in $W(\mathfrak{S}_n)$, the weak order of symmetric group $\mathfrak{S}_n$, can feel like trying to find needles in a haystack. However, through a surprising connection to the outcome map of parking functions we provide a complete characterization and enumeration for Boolean intervals in $W(\mathfrak{S}_n)$. We show that

for any $\pi\in\mathfrak{S}_n$...

Title: Number theory