Seminars and Colloquia Schedule

Some Global Relaxation Methods for Quadratic and Semidefinite Programming

Dissertation Defense
Tuesday, May 9, 2023 - 11:00 for 1.5 hours (actually 80 minutes)
Skiles 005 and ONLINE
Shengding SunGeorgia Tech

Zoom link:

Quadratic programming and semidefinite programming are vital tools in discrete and continuous optimization, with broad applications. A major challenge is to develop methodologies and algorithms to solve instances with special structures. For this purpose, we study some global relaxation techniques to quadratic and semidefinite programming, and prove theoretical properties about their qualities. In the first half we study the negative eigenvalues of $k$-locally positive semidefinite matrices, which are closely related to the sparse relaxation of semidefinite programming. In the second half we study aggregations of quadratic inequalities, a tool that can be leveraged to obtain tighter relaxation to quadratic programming than the standard Shor relaxation. In particular, our results on finiteness of aggregations can potentially lead to efficient algorithms for certain classes of quadratic programming instances with two constraints.

Dynamics of excitable cells: neurons and cardiomyocytes

Other Talks
Wednesday, May 10, 2023 - 11:00 for 1 hour (actually 50 minutes)
PLOS (second floor of Howey)
Roberto BarrioUniv. of Zaragoza
In recent years, much attention has been paid to the description of excitable media,
such as the dynamics of the brain and heart.
In both cases, the building blocks are excitable cells, neurons, and cardiomyocytes,
and a detailed look at the mathematics behind some of their mathematical models provides
a good starting point for answering some observed phenomena.
In this talk we show how some apparently  simple phenomena,
such as the spike-adding process,
have important consequences in the models and how various elements intervene behind their formation,
such as homoclinic bifurcations, fast-slow decompositions, "canards",
the completion of the Smale topological template, the formation of Morse surfaces
creating geometric bifurcations, etc.
Finally, we will illustrate its relevance in insect gait patterns and in the formation of cardiac arrhythmias.