Current contact: Brandi Henry and Rebekah Palmer

The seminar takes place on Fridays at 1:00 pm in Room 617 on the sixth floor of Wachman Hall. Pizza and refreshments are available beforehand in the lounge next door.

• Friday October 25, 2019 at 13:00, Wachman Hall 617
Lindsay Dever, Bryn Mawr College

• Friday October 18, 2019 at 13:00, Wachman Hall 617
Elie Abdo, Temple University

• Friday October 11, 2019 at 13:00, Wachman Hall 617
Khanh Le, Temple University

• Friday October 4, 2019 at 13:00, Wachman Hall 617

• Friday September 27, 2019 at 13:00, Wachman Hall 617
Rylee Lyman, Tufts University

• Friday September 13, 2019 at 13:00, Wachman Hall 617
Explicit power laws in analytic continuation problems via reproducing kernel Hilbert spaces.

Narek Hovsepyan, Temple University

Abstract: The need for analytic continuation arises frequently in the context of inverse problems. We consider several such problems and show that they exhibit a power law precision deterioration as one moves away from the source of data. We introduce a general Hilbert space-based approach for determining these exponents. The method identifies the "worst case" function as a solution of a linear integral equation of Fredholm type. In special geometries, such as the circular annulus, an ellipse or an upper half-plane the solution of the integral equation and the corresponding exponent can be found explicitly.

This is a joint work with Yury Grabovsky

• Friday September 6, 2019 at 13:00, Wachman Hall 617
Welcome Back

• Friday April 19, 2019 at 14:30, Wachman Hall 617
The Class Number One Problem

Dong Bin Choi, Temple University

Abstract: In 1952, Kurt Heegner proved (up to minor gaps) that the imaginary quadratic fields $K$ with class number $h(K) = 1$ are $\mathbb{Q}(\sqrt{d}$ with $d = -1, -2, -3, -7, -11, -19, -43, -67, -163$. To understand the problem in context, we begin from integer quadratic forms $Q(x,y) = ax^2 + bxy + cy^2$ and the question of what numbers $n$ occur as solutions to $ax^2 + bxy + cy^2 = n$ for a given $a, b, c$. This depends on the equivalence class of the quadratic form, which turns out to be closely related to ideal classes of the quadratic integer ring with discriminant $b^2 - 4ac$. We touch on some number-theoretic notions used in Heegner's proof, such as the genus of a quadratic form and the $j$-invariant of lattices. We sketch Heegner's proof (following Kezuka 2012), and conclude with solutions to some generalizations of the problem.

• Friday March 29, 2019 at 14:30, Wachman Hall 617
New off-ramp coupling conditions on the road

Najmej Salehi, Temple University

• Friday February 22, 2019 at 14:30, Wachman Hall 617
Classifying Actions of $T_n \otimes T_n$ on Path Algebras of Quivers

Delaney Aydel, Temple University

Abstract: Let $T_n$ denote the $n$th Taft algebra. We fully classify inner-faithful actions of $T_n \otimes T_n$ on four-vertex Schurian quivers as extensions of the actions of $\mathbb{Z}_n \times \mathbb{Z}_n$. One example will be presented in full, with the remaining results briefly given.

• Friday February 15, 2019 at 14:30, Wachman Hall 617
Bead Movement in Biofilms: Effects of Curli Amyloids and Analysis of Density Dependence

Brandi Henry, Temple University

• Friday February 8, 2019 at 14:30, Wachman Hall 617
Resolution of singularities

Rebekah Palmer, Temple University

Abstract: To study structures that are not quite smooth, it is convenient to transform them so that we can apply the many tools developed for smooth structures. Given a variety with singularities, we ask if there is a consistent method of transformation into a non-singular variety. In this talk, we will introduce ourselves to some varieties with singularities, demonstrate how to uniquely resolve algebraic curves, and further discuss approaches to resolving higher-dimensional varieties.

• Friday February 1, 2019 at 14:30, Wachman Hall 617
Cannon's conjecture

Thomas Ng, Temple University

Abstract: The class of all groups (even finitely generated ones) are known to have wildly inefficient, in fact often unsolvable, algorithmic properties. It is thus helpful to specialize to well-behaved subclasses. In the early 1900s Dehn studied groups as geometric objects and showed that finitely generated groups arising as the fundamental group of manifolds in dimensions less that 4 are often very algorithmically efficient. Given the existence of these well-behaved groups, one is naturally led to ask how unique they are or under what conditions are they uniquely determined. Following Gromov's notion of boundary for a hyperbolic group introduced in 1987, Cannon conjectured that for hyperbolic groups the condition that its boundary is a 2-sphere uniquely determines 3-manifold fundamental groups. In this talk we will briefly review the notions of Cayley graph, hyperbolicity, and boundary of a group. We will then survey some of the recent results that inspired and attempt to solve the Cannon conjecture.