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 Events
Idaho
Mon 20 Nov 2017, 4:00pm
Algebraic Geometry Seminar
MATH 126
Equations for surfaces in projective four-space
MATH 126
Mon 20 Nov 2017, 4:00pm-5:00pm

Abstract

This talk is concerned with the question of the minimal number of equations necessary to define a given projective variety scheme-theoretically. Every hypersurface is cut out by a single polynomial scheme-theoretically (also set-theoretically 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 n-space has codimension two, then the minimal number of polynomials necessary to cut out the variety scheme-theoretically 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 non-singular surface in projective four-space to be cut out by three polynomials. 
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Mike Irvine
Institute of Applied Mathematics, UBC
Tue 21 Nov 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Likelihood-free methods: Challenges in fitting individual-based models to epidemiological data
ESB 4133 (PIMS Lounge)
Tue 21 Nov 2017, 12:30pm-1:30pm

Abstract

Complex individual-based 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 likelihood-free 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, Markov-chain Monte Carlo and maximum likelihood. This is then applied to a complex individual-based simulation for lymphatic filariasis, a human parasitic disease, which affects over 120 million individuals internationally. Finally, I will discuss a new approach to individual-based model fitting by constructing a synthetic likelihood using mixture density networks. 
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Michal Kowalczyk
University of Chile
Tue 21 Nov 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Asymptotic stability for some nonlinear Klein-Gordon equations for odd perturbations in the energy space
ESB 2012
Tue 21 Nov 2017, 3:30pm-4:30pm

Abstract

 Showing asymptotic stability in one dimensional nonlinear Klein-Gordon 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, 4:00pm-5:00pm

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, 2:00pm-3:00pm

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, 3:00pm-4:00pm

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 self-avoiding 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 6,3-sphere and a conjecture of Suslin.
ESB 4133 (PIMS Lounge)
Wed 22 Nov 2017, 3:15pm-4:15pm

Abstract

 The algebraic K-theory, due to Quillen, of a field is related to a theory defined by Milnor called Milnor K-theory 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 (n-1)! 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, 4:00pm-5:00pm

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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