Seminars and Colloquia by Series

Embedded eigenvalues of the Neumann Poincaré operator

Series
Math Physics Seminar
Time
Thursday, April 23, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/730205379
Speaker
Wei LiLouisiana State University

The Neumann-Poincaré (NP) operator arises in boundary value problems, and plays an important role in material design, signal amplification, particle detection, etc. The spectrum of the NP operator on domains with corners was studied by Carleman before tools for rigorous discussion were created, and received a lot of attention in the past ten years. In this talk, I will present our discovery and verification of eigenvalues embedded in the continuous spectrum of this operator. The main ideas are decoupling of spaces by symmetry and construction of approximate eigenvalues. This is based on two works with Stephen Shipman and Karl-Mikael Perfekt.

Numerical Estimates for Arm Exponents and the Acceptance Profile of Invasion Percolation

Series
Dissertation Defense
Time
Thursday, April 23, 2020 - 14:00 for 2 hours
Location
Online via BlueJeans: https://bluejeans.com/127628065?src=calendarLink
Speaker
Jiaheng LiSchool of Mathematics

The main work of this thesis is to numerically estimate some conjectured arm exponents when there exist certain number of open paths and closed dual paths that extend to the boundary of a box of sidelength N centering at the origin in bond invasion percolation on a plane square lattice by Monte-Carlo simulations. The result turns out to be supportive for the conjectured value. The numerical estimate for the acceptance profile of invasion percolation at the critical point is also obtained. An efficient algorithm to simulate invasion percolation and to find disjoint paths on most regular 2-dimensional lattices are also discussed. 

Bordered Floer Homology via Immersed Curves

Series
Geometry Topology Student Seminar
Time
Wednesday, April 22, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Online
Speaker
Sally CollinsGeorgia Tech

In the setting of manifolds with connected torus boundary, we can reinterpret bordered invariants as immersed curves in the once punctured torus. This machinery, due to Hanselman, Rasmussen, and Watson, is particularly useful in the context of knot complements. We will show how a type D structure can be viewed as a multicurve in the boundary of a manifold, and we will consider how the operation of cabling acts on this new invariant. If time permits, we will discuss how to extract concordance invariants from the curves.

Cancelled

Series
Analysis Seminar
Time
Wednesday, April 22, 2020 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker

Finding and cerifying roots of systems of equations

Series
Dissertation Defense
Time
Tuesday, April 21, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
https://gatech.bluejeans.com/481175204
Speaker
Kisun LeeGeorgia Tech

Numerical algebraic geometry studies methods to approach problems in algebraic geometry numerically. Especially, finding roots of systems of equations using theory in algebraic geometry involves symbolic algorithm which requires expensive computations, numerical techniques often provides faster methods to tackle these problems. We establish numerical techniques to approximate roots of systems of equations and ways to certify its correctness.

As techniques for approximating roots of systems of equations, homotopy continuation method will be introduced. Combining homotopy method with monodromy group action, we introduce techniques for solving parametrized polynomial systems. Since numerical approaches rely on heuristic method, we study how to certify numerical roots of systems of equations. Based on Newton’s method, we study Krawczyk method and Smale’s alpha theory. These two method will be mainly used for certifying regular roots of systems. Furthermore, as an approach for multiple roots, we establish the local separation bound of a multiple root. For multiple roots whose deflation process terminates by only one iteration, we give their local separation bound and study how to certify an approximation of such multiple roots.

 

All lines on a smooth cubic surface in terms of three skew lines

Series
Algebra Seminar
Time
Monday, April 20, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tianyi ZhangGeorgia Tech
Harris showed that the incidence variety of a smooth cubic surface containing 27 lines has solvable Galois group over the incidence variety of a smooth cubic surface containing 3 skew lines. It follows that for any smooth cubic surface, there exist formulas for all 27 lines in terms of any 3 skew lines. I will briefly talk about Harris' results and how Stephen, Daniel, and I compute these formulas explicitly.
 

The talk will be held online via Bluejeans, use the following link to join the meeting.

TBA by Jeffrey Rosenthal

Series
Combinatorics Seminar
Time
Friday, April 17, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jeffrey RosenthalUniversity of Toronto

TBA (joint with Stochastics Seminar)

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