EveryTopic Seminar, Spring 2019


Thursdays 12:00-1:00pm, Goldsmith 300.
Organizers: Corey Bregman, Konstantin Matveev.

The EveryTopic Seminar is the Brandeis math department colloquium. Talks are 50 minutes long and aimed at a broad audience of mathematicians.

Date

Speaker (Affiliation)

Title

Abstract

Jan 24

David Lipshutz (Technion) 

Synchronous oscillatory behavior for systems of coupled delay differential equations  

Dynamical system models with delayed negative feedback arise in a wide variety of applications in science and engineering, ranging from models of neuronal networks to Internet rate control models. In some applications, synchronous stable periodic oscillatory behavior can be critical to the well functioning of a system; and in other applications, it can represent systemic failure. In the first part of this talk we consider a prototypical one-dimensional delay differential equation (DDE) with a negative feedback condition and we review prior work on existence, uniqueness, and stability of periodic oscillatory solutions of this DDE. In the second part of the talk we discuss synchronous periodic oscillatory solutions of a system of coupled DDEs. Interestingly, we show that under conditions where the one-dimensional system exhibits stable periodic oscillatory behavior, the stability of the synchronous periodic solution depends on the spectrum of the coupling matrix. 

Jan 31

No Speaker 

 

 

Feb 7

No Speaker 

 

 

Feb 14

TBA 

 

 

Feb 21

Spring Break 

 

 

Feb 28

Daniel Álvarez-Gavela (IAS) 

Lagrangian and Legendrian manifolds from the viewpoint of parametric Morse theory 

Lagrangian (resp. Legendrian) submanifolds of symplectic (resp. contact) manifolds exhibit rigidity phenomena arising from the presence of subtle pseudo-holomorphic curve invariants. When the symplectic (resp. contact) manifold is a cotangent bundle (resp. 1-jet space) many of these rigidity phenomena can be recovered from the viewpoint of parametrized (finite dimensional) Morse theory. Indeed, the generating function construction produces an immersed Lagrangian (resp. embedded Legendrian) submanifold out of any family of functions parametrized by the base of the cotangent bundle (resp. 1-jet space). In this talk we will explain the generating function construction and give a sampling of its implications, including some hopes and dreams. 

Mar 7

TBA 

 

Mar 14

Denis Patterson 

Spatially extended ecological models

 

Located mainly in the tropics, Savannas cover around 20% of the Earths landmass and their interaction with another ecologically vital biome, tropical forest, is the subject of significant interest from the point of view of conservation. The Staver-Levin mean-field model is a widely studied and phenomenologically rich system of ODEs describing the interactions of savanna, grasslands and tropical forest. I will discuss ongoing work in which we derive appropriate spatial extensions of this important model from probabilistic foundations and analyze the behavior of the resulting spatial models. In particular, we show that Turing-type pattern formation is not possible unless resource constraints are present and that a linear rainfall gradient across the spatial domain can induce novel behaviors which merit further study (on both practical and theoretical grounds). This is joint work with Jonathan Touboul, Carla Staver (Yale) and Simon Levin (Princeton).

Mar 21

TBA 

 

 

Mar 28

TBA 

 

 

Apr 4

TBA

Apr 11

TBA

Apr 18

Michael Ben-Zvi (Tufts)

A combination theorem for CAT(0) groups and their boundaries

Often in mathematics, we study an object by breaking it down into easier-to-understand pieces. A combination theorem is a result which says if we know something about the pieces and how they fit together, we can say something about the bigger object. I will discuss a combination theorem for one-ended CAT(0) groups and their boundaries, and will do so through a number of examples.

Tuesday, Apr 30

Amit Shah (University of Leeds)

Cluster categories and partial cluster-tilted algebras

In this talk, I will first try to indicate why some people care about cluster algebras and cluster categories. Then I will focus on a specific cluster category, namely the cluster category coming from a Dynkin graph of type A. Although the formal definition for a cluster category can look a bit intimidating, we will see that the category has a nice Auslander-Reiten quiver — pictorial description of the category — (at least for type A) and so can be easily understood. Hopefully there will be time to give the definition of a partial cluster-tilted algebra, give an idea of how I’ve been trying to study them.


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Fall 2018 


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