Seminars and Colloquia by Series

Generation and Synchronization of Oscillations in Synthetic Gene Networks

Series
Mathematical Biology Seminar
Time
Wednesday, April 17, 2013 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles Bldg, Room 006
Speaker
Lev Tsimring – UC San Diego, BIOCircuits Inst.
In this talk, I will describe our recent experimental and theoretical work on small synthetic gene networks exhibiting oscillatory behavior. Most living organisms use internal genetic "clocks" to govern fundamental cellular behavior. While the gene networks that produce oscillatory expression signals are typically quite complicated, certain recurring network motifs are often found at the core of these biological clocks. One common motif which may lead to oscillations is delayed auto-repression. We constructed a synthetic two-gene oscillator based on this design principle, and observed robust and tunable oscillations in bacteria. Computational modeling and theoretical analysis show that the key mechanism of oscillations is a small delay in the negative feedback loop. In a strongly nonlinear regime, this time delay can lead to long-period oscillations that can be characterized by "degrade and fire'' dynamics. We also achieved synchronization of synthetic gene oscillators across cell population as well as multiple populations using variants of the same design in which oscillators are synchronized by chemical signals diffusing through cell membranes and throughout the populations.

Athens-Atlanta number theory seminar 2 - Arithmetic statistics over function fields

Series
Algebra Seminar
Time
Tuesday, April 16, 2013 - 17:15 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jordan Ellenberg – University of Wisconsin
What is the probability that a random integer is squarefree? Prime? How many number fields of degree d are there with discriminant at most X? What does the class group of a random quadratic field look like? These questions, and many more like them, are part of the very active subject of arithmetic statistics. Many aspects of the subject are well-understood, but many more remain the subject of conjectures, by Cohen-Lenstra, Malle, Bhargava, Batyrev-Manin, and others. In this talk, I explain what arithmetic statistics looks like when we start from the field Fq(x) of rational functions over a finite field instead of the field Q of rational numbers. The analogy between function fields and number fields has been a rich source of insights throughout the modern history of number theory. In this setting, the analogy reveals a surprising relationship between conjectures in number theory and conjectures in topology about stable cohomology of moduli spaces, especially spaces related to Artin's braid group. I will discuss some recent work in this area, in which new theorems about the topology of moduli spaces lead to proofs of arithmetic conjectures over function fields, and to new, topologically motivated questions about counting arithmetic objects.

The Ruelle zeta for C^\infty Anosov flows

Series
CDSNS Colloquium
Time
Tuesday, April 16, 2013 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Mark Pollicott – Univ. of Warwick
In joint work with P. Guilietti and C. Liverani, we show that the Ruelle zeta function for C^\infty Anosov flows has a meromorphic extension to the entire complex plane. This generalises results of Selberg (for geodesic flows in constant curvature) and Ruelle. I

Athens-Atlanta number theory seminar 1 - The arithmetic of hyperelliptic curves

Series
Algebra Seminar
Time
Tuesday, April 16, 2013 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dick Gross – Harvard University
Hyperelliptic curves over Q have equations of the form y^2 = F(x), where F(x) is a polynomial with rational coefficients which has simple roots over the complex numbers. When the degree of F(x) is at least 5, the genus of the hyperelliptic curve is at least 2 and Faltings has proved that there are only finitely many rational solutions. In this talk, I will describe methods which Manjul Bhargava and I have developed to quantify this result, on average.

Asymptotic behavior of globally modified non-autonomous 3D Navier-Stokes equations with memory effects and stochastic perturbations

Series
PDE Seminar
Time
Tuesday, April 16, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Chen, Zhang – Shandong University
In this talk, globally modified non-autonomous 3D Navier-Stokes equations with memory and perturbations of additive noise will be discussed. Through providing theorem on the global well-posedness of the weak and strong solutions for the specific Navier-Stokes equations, random dynamical system (continuous cocycle) is established, which is associated with the above stochastic differential equations. Moreover, theoretical results show that the established random dynamical system possesses a unique compact random attractor in the space of C_H, which is periodic under certain conditions and upper semicontinuous with respect to noise intensity parameter.

The rank of elliptic curves

Series
School of Mathematics Colloquium
Time
Tuesday, April 16, 2013 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Benedict Gross – Harvard University
The problem of finding rational solutions to cubic equations is central in number theory, and goes back to Fermat. I will discuss why these equations are particularly interesting, and the modern theory of elliptic curves that has developed over the past century, including the Mordell-Weil theorem and the conjecture of Birch and Swinnerton-Dyer. I will end with a description of some recent results of Manjul Bhargava on the average rank.

Stark-Heegner/Darmon points on elliptic curves over totally real fields

Series
Algebra Seminar
Time
Monday, April 15, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Amod Agashe – Florida State University –
The classical theory of complex multiplication predicts the existence of certain points called Heegner points defined over quadratic imaginary fields on elliptic curves (the curves themselves are defined over the rational numbers). Henri Darmon observed that under certain conditions, the Birch and Swinnerton-Dyer conjecture predicts the existence of points of infinite order defined over real quadratic fields on elliptic curves, and under such conditions, came up with a conjectural construction of such points, which he called Stark-Heegner points. Later, he and others (especially Greenberg and Gartner) extended this construction to many other number fields, and the points constructed have often been called Darmon points. We will outline a general construction of Stark-Heegner/Darmon points defined over quadratic extensions of totally real fields (subject to some mild restrictions) that combines past constructions; this is joint work with Mak Trifkovic.

Central-Upwind Schemes for Shallow Water Models

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 15, 2013 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alexander Kurganov – Tulane University
I will first give a brief review on simple and robust central-upwind schemes for hyperbolic conservation laws. I will then discuss their application to the Saint-Venant system of shallow water equations. This can be done in a straightforward manner, but then the resulting scheme may suffer from the lack of balance between the fluxes and (possibly singular) geometric source term, which may lead to a so-called numerical storm, and from appearance of negative values of the water height, which may destroy the entire computed solution. To circumvent these difficulties, we have developed a special technique, which guarantees that the designed second-order central-upwind scheme is both well-balanced and positivity preserving. Finally, I will show how the scheme can be extended to the two-layer shallow water equations and to the Savage-Hutter type model of submarine landslides and generated tsunami waves, which, in addition to the geometric source term, contain nonconservative interlayer exchange terms. It is well-known that such terms, which arise in many different multiphase models, are extremely sensitive to a particular choice their numerical discretization. To circumvent this difficulty, we rewrite the studied systems in a different way so that the nonconservative terms are multiplied by a quantity, which is, in all practically meaningful cases, very small. We then apply the central-upwind scheme to the rewritten system and demonstrate robustness and superb performance of the proposed method on a number numerical examples.

Legendrian contact homology and products of Legendrian knots

Series
Geometry Topology Seminar
Time
Monday, April 15, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Peter Lambert-Cole – LSU
Legendrian contact homology is an invariant in contact geometry that assigns to each Legendrian submanifold a dg-algebra. While well-defined, it depends upon counts of holomorphic curves that can be hard to calculate in practice. In this talk, we introduce a class of Legendrian tori constructed as the product of collections of Legendrian knots. For this class, we discuss how to explicitly compute the dg-algebra invariant of the tori in terms of diagram projections of the constituent Legendrian knots.

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