Idaho

Mon 20 Nov 2017, 4:00pm
Algebraic Geometry Seminar
MATH 126

Equations for surfaces in projective fourspace

MATH 126
Mon 20 Nov 2017, 4:00pm5:00pm
Abstract
This talk is concerned with the question of the minimal number of equations necessary to define a given projective variety schemetheoretically. Every hypersurface is cut out by a single polynomial schemetheoretically (also settheoretically and ideal theoretically). Therefore the question is more interesting if a variety has a higher codimension. In this talk, we focus on the case when the codimension is two. If a variety in projective nspace has codimension two, then the minimal number of polynomials necessary to cut out the variety schemetheoretically is between 2 and n+1. However the varieties cut out by fewer than n+1, but more than 2 polynomials seem very rare. The main goal of this talk is to discuss conditions for a nonsingular surface in projective fourspace to be cut out by three polynomials.
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Institute of Applied Mathematics, UBC

Tue 21 Nov 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Likelihoodfree methods: Challenges in fitting individualbased models to epidemiological data

ESB 4133 (PIMS Lounge)
Tue 21 Nov 2017, 12:30pm1:30pm
Abstract
Complex individualbased models abound in epidemiology and ecology. Fitting these models to data is a challenging problem: methodologies can be inaccessible to all but specialists, there may be challenges in adequately describing uncertainty in model fitting, and the complex models may take a long time to run, requiring parameter selection procedures. Approximate Bayesian Computation has been proposed as a likelihoodfree method in resolving these issues, however requires careful selection of summary statistics and annealing scheme. I compare this procedure directly to standard methodologies where the likelihood exists, Markovchain Monte Carlo and maximum likelihood. This is then applied to a complex individualbased simulation for lymphatic filariasis, a human parasitic disease, which affects over 120 million individuals internationally. Finally, I will discuss a new approach to individualbased model fitting by constructing a synthetic likelihood using mixture density networks.
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University of Chile

Tue 21 Nov 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Asymptotic stability for some nonlinear KleinGordon equations for odd perturbations in the energy space

ESB 2012
Tue 21 Nov 2017, 3:30pm4:30pm
Abstract
Showing asymptotic stability in one dimensional nonlinear KleinGordon equations is a notoriously difficult problem. In this talk I will describe an approach based on virial estimates which allows to prove it in case when only odd perturbations are allowed. In particular I will discuss asymptotic stability of the kink in the \phi^{^4} model.
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Brown University

Tue 21 Nov 2017, 4:00pm
SPECIAL
Algebraic Geometry Seminar
MATH 126

The Picard group of the moduli of smooth complete intersections of two quadrics

MATH 126
Tue 21 Nov 2017, 4:00pm5:00pm
Abstract
We study the moduli space of smooth complete intersections of two quadrics by relating it to the geometry of the singular members of the corresponding pencil. We give a new description for this parameter space by using the fact that two quadrics can be simultaneously diagonalized. Using this description we can compute the Picard group, which always happens to be cyclic. For example, we show that the Picard group of the moduli stack of smooth degree 4 Del Pezzo surfaces is Z/4Z.
This is a joint work with Giovanni Inchiostro.
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UBC, Math

Wed 22 Nov 2017, 2:00pm
Mathematical Biology Seminar
PIMS (ESB 4th floor)

Pattern formation on a Slowly Flattening Spherical Cap: A closest Point Method Approach.

PIMS (ESB 4th floor)
Wed 22 Nov 2017, 2:00pm3:00pm
Abstract
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UBC

Wed 22 Nov 2017, 3:00pm
Probability Seminar
ESB 2012

Spin systems and some natural questions in probability

ESB 2012
Wed 22 Nov 2017, 3:00pm4:00pm
Abstract
It has long been known that many interesting questions in probability have a formulation in the language of spin systems. However, it has been only rather recently that the methods developed for spin systems were applied to finally obtain answers to some of these questions. In this talk, I will discuss three such questions, about the weakly selfavoiding walk, the vertex reinforced jump process, and random band matrices. I will then show the audience some technical lemmas that are at the heart of the analysis of spin systems.
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UBC

Wed 22 Nov 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)

The A1 calculation of the 4th homotopy group of the 6,3sphere and a conjecture of Suslin.

ESB 4133 (PIMS Lounge)
Wed 22 Nov 2017, 3:15pm4:15pm
Abstract
The algebraic Ktheory, due to Quillen, of a field is related to a theory defined by Milnor called Milnor Ktheory and denoted K^M. In the 1980s, Andrei Suslin constructed a map K_n(F) > K^M_n(F), and conjectured that the image was the subgroup (n1)! K^M_n(F). He also proved the conjecture for n<=3. For n=5, we reinterpret the construction as a construction in the A1 homotopy groups of spheres and BGL, and by calculating these groups, show that the conjecture is true in this case as well. This represents part of a joint project with Aravind Asok, Jean Fasel and Kirsten Wickelgren.
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Texas A&M

Thu 23 Nov 2017, 4:00pm
SPECIAL
Algebraic Geometry Seminar
MATX 1102

Irrational Toric Varieties

MATX 1102
Thu 23 Nov 2017, 4:00pm5:00pm
Abstract
Classical toric varieties come in two flavours: Normal toric varieties are given by rational fans in R^n. A (not necessarily normal) affine toric variety is given by finite subset A of Z^n. When A is homogeneous, it is projective. Applications of mathematics have long studied the positive real part of a toric variety as the main object, where the points A may be arbitrary points in R^n. For example, in 1963 Birch showed that such an irrational toric variety is homeomorphic to the convex hull of the set A.
Recent work showing that all Hausdorff limits of translates of irrational toric varieties are toric degenerations suggested the need for a theory of irrational toric varieties associated to arbitrary fans in R^n. These are R^n_>equivariant cell complexes dual to the fan. Among the pleasing parallels with the classical theory is that the space of Hausdorff limits of the irrational projective toric variety of a finite set A in R^n is homeomorphic to the secondary polytope of A.
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