Department of Mathematics
Mathematics Colloquium
Organizer Mailing list: https://groups.google.com/forum/#!forum/ccnymathcolloquium/joinThe Mathematics Department Colloquium typically meets on Thursdays from 12:30 pm to 1:20 pm in NAC 6/114. This will typically be preceded by tea and coffee at noon in the math lounge, and will be followed by lunch. To receive announcements via email, please join our google group
Upcoming talks

Thursday, May 09, 2019, 12:30PM, NAC 6/114
Linda Keen (Lehman College (CUNY)), TBATBA
Most recent talks

Thursday, March 28, 2019, 12:30PM, NAC 6/114
Konstantin Mischaikow (Rutgers U.), A combinatorial/algebraic topological approach to nonlinear dynamicsMotivated by the increase in data driven science I will discuss a combinatorial/algebraic topological approach to characterizing nonlinear dynamics. In particular, I will describe how order theory can be used to efficiently and effectively organize the decomposition of dynamics and how algebraic topological tools can be used to characterize the structure of the dynamics. I will then propose a definition of nonlinear dynamics based on these structures. To demonstrate the effectiveness of this approach I will consider several problems from systems and synthetic biology. I will focus on identification and rejection of network models for these types of systems based on functional form and time series data.

Thursday, March 21, 2019, 12:30PM, NAC 6/114
Yung Choi (U. Conn), Stationary and traveling waves of the FitzHughNagumo EquationsThe talk will be structured for general colloquium audience.
Stationary waves are steady state solutions in unbounded domain, while traveling waves will appear steady when viewed in a moving frame. We start with stationary waves of a scalar reactiondiffusion equation, as they can be easily explained using a phase plane analysis. Next we survey some results on the FitzHughNagumo system. For some special parameter regimes, the solutions give discontinuous jump profiles as a certain parameter epsilon goes to zero. This can be analyzed using Γconvergence and gives rise to a geometric variational problem; its radially symmetric solutions (known as bubbles) and their local stability are completely classified for all parameters.
We next turn our attention to traveling waves. Again we start with a scalar equation and work towards the FitzHughNagumo systems. The use of a Γconvergence analysis to traveling wave has recently been achieved. It seems to be the first instance of extending this kind of analysis to nonstationary problems.

Thursday, February 21, 2019, 12:30PM, NAC 6/114
Vincent Martinez (Hunter College (CUNY)), Studies in analyticity for hydrodynamic and chemotaxis modelsIn their 1987 seminal paper, Foias and Temam established analyticity in both space and time for solutions of the two(2D) and threedimensional (3D) NavierStokes equations (NSE) by developing an energy method now known as the technique of Gevreynorms, i.e., a norm which characterizes real analyticity of a function. This approach has since become standard for establishing spatial analyticity of solutions to various parabolictype equations. In this talk, we shed light on the relation between the structure of the equation and its wellposedness theory in various analytic Gevreynorm regularity classes. We do so in the context of the supercritical SQG equation, the KellerSegel equation, and a coupled chemotaxishydrodynamic model through the notion of “criticality.”