Events for the week of March 12 2012 Monday Mar 12  16:3018:00  Participating Number Theory Seminar (MS 5117)   Ashay Burungale (UCLA)  On the weak JacquetLanglands correspondence  Abstract. Automorphic representations of a quaternion algebra over
a number field F correspond to certain automorphic representations of GL_2(F). Following an article of Knapp and Rogawski, we will sketch a proof of this result using the trace formula.  Tuesday Mar 13  15:0015:50  Participating Analysis Seminar (MS6221)   Sam Xu (UCLA)  Some TimeDependent Parabolic PDEs
 16:0016:50  Special Applied Math Seminar (MS 5118)   Mark Lewis (University of Alberta)  Mathematical Models for Carnivore Territories  Abstract. Social carnivores, such as wolves and coyotes, have
distinct and welldefined home ranges. During the formation
of these home ranges scent marks provide important cues
regarding the use of space by familiar and foreign packs.
In this talk I will propose a set of mechanistic rules that
can be used to understand the process of territorial
pattern formation through interactions with scent marks.
I will consider different model formulations, with and without the
den site as an organizing centre for spatial movement. Under
realistic assumptions the resulting territorial patterns include
spontaneous formation of `buffer zones' between territories
which act refuges for prey such as deer. This is supported by
detailed radiotracking studies. The model will also be
analysed using game theory, where the objective of each pack is to
maximize its fitness by increasing intake of prey (deer) and by
decreasing interactions with hostile neighboring packs. Predictions
will compared with radio tracking data for wolves and coyotes.  16:3017:20  Participating Analysis Seminar (MS6221)   John Garnett (UCLA)  Beurling Malliavin theory
 Wednesday Mar 14  15:0017:00  Topology Seminar (MS 5137)   Sam Lewallen (Princeton U.)  Symplectic Knot Invariants from SU(2) Representations  16:0016:50  Probability Seminar (MS 6229)   William I. Newman (UCLA)  Order in Chaos: The Emergence of Pattern in Random Processes  Abstract. Many years ago, Mark Kac was consulted by colleague Lamont Cole regarding fieldbased observations of animal populations that suggested the existence of 34 year cycles in going from peak to peak. Kac provided an elegant argument for how purely random sequences of numbers could yield a mean value of 3 years, thereby establishing the notion that pattern can seemingly emerge in random processes. (This does not, however, mean that there could be a largely deterministic cause of such population cycles.)
By extending Kac's argument, we show how the distribution of cycle length can be analytically established using methods derived from random graph theory, etc. We will examine how such distributions emerge in other natural settings, including large earthquakes as well as colored Brownian noise and other random models and, for amusement, the Standard & Poor's 500 index for percent daily change from 1928 to the present.
We then show how this random model could be relevant to a variety of spatiallydependent problems and the emergence of clusters, as well as to memory and the aphorism "bad news comes in threes." The derivation here is remarkably similar to the former and yields some intriguing closedform results. Importantly, the centroids or "centers of mass" of these clusters also yields clusters and a hierarchy then emerges. Certain "universal" scalings appear to emerge and scaling factors reminiscent of Feigenbaum numbers. Finally, as one moves from one dimension to 2, 3, and 4 dimensions, the scaling behaviors undergo modest change leaving this scaling phenomena qualitatively intact.  16:0016:50  Joint Applied Math/Probability Seminar (MS 6229)   William I. Newman (UCLA)  Order in Chaos: The Emergence of Pattern in Random Processes  Abstract. Many years ago, Mark Kac was consulted by colleague Lamont Cole regarding fieldbased observations of animal populations that suggested the existence of 34 year cycles in going from peak to peak. Kac provided an elegant argument for how purely random sequences of numbers could yield a mean value of 3 years, thereby establishing the notion that pattern can seemingly emerge in random processes. (This does not, however, mean that there could be a largely deterministic cause of such population cycles.)
By extending Kac's argument, we show how the distribution of cycle length can be analytically established using methods derived from random graph theory, etc. We will examine how such distributions emerge in other natural settings, including large earthquakes as well as colored Brownian noise and other random models and, for amusement, the Standard & Poor's 500 index for percent daily change from 1928 to the present.
We then show how this random model could be relevant to a variety of spatiallydependent problems and the emergence of clusters, as well as to memory and the aphorism "bad news comes in threes." The derivation here is remarkably similar to the former and yields some intriguing closedform results. Importantly, the centroids or "centers of mass" of these clusters also yields clusters and a hierarchy then emerges. Certain "universal" scalings appear to emerge and scaling factors reminiscent of Feigenbaum numbers. Finally, as one moves from one dimension to 2, 3, and 4 dimensions, the scaling behaviors undergo modest change leaving this scaling phenomena qualitatively intact.  Thursday Mar 15  13:5014:50  Combinatorics Seminar (MS 7608)   Choongbum Lee (UCLA)  Large and judicious bisections of graphs  Abstract. It is very well known that every graph on n vertices and m edges
admits a bipartition of size at least m/2. This bound can be
improved to m/2 + (n1)/4 for connected graphs, and m/2 + n/6 for
graphs without isolated vertices, as proved by Edwards, and Erdos,
Gyarfas, and Kohayakawa, respectively. A bisection of a graph is a
bipartition in which the size of the two parts differ by at most 1. We
prove that graphs with maximum degree o(n) in fact admit a bisection
which asymptotically achieves the above bounds.
These results follow from a more general theorem, which can also be
used to answer several questions and conjectures of Bollobas and
Scott on judicious bisections of graphs.
Joint work with PoShen Loh and Benny Sudakov  17:1518:15  GSO Seminar (MS 6620)   Yingkun Li (UCLA)  Congruent Numbers and Elliptic Curves  Abstract. Congruent numbers are integers, which can be realized as the
area of a right triangle with rational sides. It's an ancient problem
to list all congruent numbers, and is still more or less open today. In
this talk, we will look at the connection between congruent numbers
and elliptic curves, and theorems about the former obtained via
studying the latter.  Friday Mar 16  15:0016:40  Algebra Seminar (MS 7608)   Beren Sanders (UCLA)  Quiver representations VII.  15:0015:50  Analysis and PDE Seminar (MS 6221)   Jun Kitagawa (Univ. British Columbia)  Regularity for the Optimal Transport Problem on the Embedded
Sphere When Standard Conditions Fail
 Abstract. We consider regularity for Monge solutions to the optimal
transport problem when the initial and target measures are supported
on the embedded sphere, and the cost function is the Euclidean
distance squared. Gangbo and McCann have shown that when the initial
and target measures are supported on boundaries of strictly convex
domains in $\mathbb{R}^n$, there is a unique Kantorovich solution, but
it can fail to be a Monge solution. In the case when we are dealing
with the sphere with measures absolutely continuous with respect to
surface measure, we present two different types of conditions on the
densities of the measures to ensure that the solution given by Gangbo
and McCann is indeed a Monge solution, and obtain higher regularity as
well. This talk is based on joint work with Micah Warren. 
