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 Events
UBC
Mon 20 Oct 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Donaldson-Thomas theory of local elliptic surfaces via the topological vertex
ESB 4127 (host: UBC)
Mon 20 Oct 2014, 3:00pm-4:00pm

Abstract

Donaldson-Thomas (DT) invariants of a Calabi-Yau threefold X are fundamental quantum invariants given by (weighted) Euler characteristics of the Hilbert schemes of X. We compute these invariants for the case where X is a so-called local elliptic surface --- it is the total space of the canonical line bundle over an elliptic surface. We find that the generating functions for the invariants admit a nice product structure. We introduce a new technique which allows us to use the topological vertex in this computation --- a tool which previously could only be used for toric threefolds. As a by product, we discover surprising new identities for the topological vertex. This is joint work with Martijn Kool, with an assist from Ben Young. 

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Yonsei University, visiting UC-Irvine
Mon 20 Oct 2014, 3:00pm
Harmonic Analysis Seminar
Math 204
Oscillatory integrals and Newton polyhedra
Math 204
Mon 20 Oct 2014, 3:00pm-4:00pm

Abstract


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Mark Schmidt
Computer Science, UBC
Tue 21 Oct 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS lounge)
Minimizing Finite Sums with the Stochastic Average Gradient
ESB 4133 (PIMS lounge)
Tue 21 Oct 2014, 12:30pm-1:30pm

Abstract

We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in the sum. However, by incorporating a memory of previous gradient values the SAG method achieves a faster convergence rate than black-box SG methods. Specifically, under standard assumptions the convergence rate is improved from O(1/k) to a linear convergence rate of the form O(p^k) for some p < 1. Further, in many cases the convergence rate of the new method is also faster than black-box deterministic gradient methods, in terms of the number of gradient evaluations. Beyond these theoretical results, the algorithm also has a variety of appealing practical properties: it supports regularization and sparse datasets, it allows an adaptive step-size and has a termination criterion, it allows mini-batches, and its performance can be further improved by non-uniform sampling. Numerical experiments indicate that the new algorithm often dramatically outperforms existing SG and deterministic gradient methods, and that the performance may be further improved through the use of non-uniform sampling strategies.

Note for Attendees

Sushi will be provided.
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Eva Czabarka
University of South Carolina
Tue 21 Oct 2014, 3:00pm
Discrete Math Seminar
ESB 4127
Mixed orthogonal arrays and more - part Sperner families
ESB 4127
Tue 21 Oct 2014, 3:00pm-4:00pm

Abstract

Sperner's theorem from 1928 states that the greatest number subsets of an n-element set such that no subset contains another (in other words the largest chain is length 1), is \binom{n}{\lfloor n/2\rfloor}. This result has many generalizations since: L-Sperner families are families where the largest chain is of length at most L, M-part families are families where there is no chain of length 2 where the increase of a chain is contained in a fixed M-partition of the underlying set, etc. Mixed orthogonal arrays are designs introduced by statisticians for designing experiments, so that factors potentially influential to the outcome occur simultaneously in a regular manner. We show that these distant topics have a strong connection (in particular mixed ortogonal arrays and homogeneous M-part (L_1,...,L_M)-Sperner families correspond to each other), and provide constructions for mixed orthogonal arrays. Joint work with H Aydinian and L.A. Szekely.
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Tingting Huan
UBC
Tue 21 Oct 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Traveling fronts to reaction diffusion equations with fractional Laplacian
ESB 2012
Tue 21 Oct 2014, 3:30pm-4:30pm

Abstract

We show the nonexistence of traveling fronts in the combustion model with fractional Laplacian (-\Delta)^s when s\in(0,1/2]. Our method can be used to give a direct and simple proof of the nonexistence of traveling fronts for the usual Fisher-KPP nonlinearity. Also we prove the existence and nonexistence of traveling waves solutions for different ranges of the fractional power s for the generalized Fisher-KPP type model. 
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UAlberta
Wed 22 Oct 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
Equivalences of derived categories of double mirrors
ESB 4127 (host: UAlberta)
Wed 22 Oct 2014, 3:00pm-4:00pm

Abstract

Given a Calabi-Yau complete intersection in a toric Fano variety, there are various ways to construct the mirror. Sometimes these mirrors are isomorphic and sometimes they are not. These distinct 'double' mirrors should be equivalent in some way if they all have a shot at being the 'correct' mirror in some setting of mirror symmetry. We will discuss the Batyrev-Borisov and Berglund-Hübsch-Krawitz construction and the double mirrors which arise, as well as their relationship through variation of geometric invariant theory quotients, Landau-Ginzburg models, and derived equivalence. This is joint work with Tyler Kelly.
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Tom Hutchcroft
UBC
Wed 22 Oct 2014, 3:00pm
Probability Seminar
ESB 2012
Unimodular hyperbolic triangulations
ESB 2012
Wed 22 Oct 2014, 3:00pm-4:00pm

Abstract

For deterministic bounded degree triangulations, circle packing has proven a powerful tool for studying random walk via geometric arguments. In this talk, I will discuss extensions and analogues for random triangulations without the assumption of bounded degree. In particular, I will show that the circle packing type (hyperbolic or Euclidean) is determined by the expected degree at the root and that, in the hyperbolic case, the geometric boundary given by the circle packing coincides with the Poisson boundary of the random walk. No specialised knowledge will be assumed and I will review the main examples.
Joint work with Omer Angel, Asaf Nachmias and Gourab Ray.
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UBC
Wed 22 Oct 2014, 3:00pm
Undergraduate Colloquium
MATH 203
The Art in Problem Solving
MATH 203
Wed 22 Oct 2014, 3:00pm-4:00pm

Abstract

The scope of what constitutes a math problem is far wider than "how many apples are left in the basket if..." or "prove the equation has at least one real root." Math problems can be seen in everything from the development of bone structures through the bending of light due to massive objects; math is everywhere. By going through a few projects I've recently had the fortune of working on, I want to highlight a few of the beautiful ways mathematical thinking finds its way into solving real-world problems including: using physical modelling in designing devices for water filtration by electrodialysis, implementing formal asymptotic analysis to predict the behaviour of a fusion reactor, and writing numerical methods to provide a proof-of-concept for a new method of mass spectrometry. Just as there is art in expressing the world through imagery and poetry, so there is in analyzing problems appropriately and making use of such analysis.  No prior knowledge is expected: all the problems presented will include the relevant background information.
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UBC
Wed 22 Oct 2014, 3:15pm
Topology and related seminars
ESB 4133
Generalized torsion in knot groups
ESB 4133
Wed 22 Oct 2014, 3:15pm-4:15pm

Abstract

Classical knot groups, that is fundamental groups of knot complements in 3-space, are known to be torsion-free.  However, we show that for many knots, their groups contain generalized torsion: a nontrivial element such that some product of conjugates of that element equals the identity.  One example (the hyperbilic knot 5_2) was discovered with the aid of a Python program written by the USRA student Geoff Naylor.  Other examples include torus knots, algebraic knots in the sense of Milnor (arising from singularities of complex curves) and satellites of knots whose groups contain generalized torsion.  Although all knot groups are left-orderable, the existence of generalized torsion is an obstruction to their being bi-orderable.
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Abdul Kara
University of the Witwatersrand, Johannesburg
Wed 22 Oct 2014, 3:30pm
Symmetries and Differential Equations Seminar
MATH 126
Symmetry structures of manifolds
MATH 126
Wed 22 Oct 2014, 3:30pm-4:30pm

Abstract

We study the Noether and Lie symmetries that arise from the Euler-Lagrange equations, i.e., the ‘geodesic’ equations, related to manifolds that arise from a metric. In particular and as one of the examples, we present some peculiarities associated with the ASD Ricci-flat metric which depends on the `second heavenly equation'. It is noted, in general, that the Killing vectors are contained in the Noether symmetries generated by the Lagrangian of the geodesic equations. Specifically, a number of symmetries which are Noether and not Killing vectors are independent of the arc length variable ‘s’.
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Foster Tom
UBC
Thu 23 Oct 2014, 12:30pm
Graduate Student Seminar
Math 225
The probabilistic method
Math 225
Thu 23 Oct 2014, 12:30pm-1:45pm

Abstract

The probabilistic method, pioneered by Paul Erdős, is a means of proving the existence of a certain object. By describing a random process of choosing objects, if there is a nonzero probability of making a successful choice, then necessarily the desired kind of object exists. We present a problem in discrete math that employs this method.
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Avi Kulkarni
SFU
Thu 23 Oct 2014, 3:30pm
Number Theory Seminar
room ASB 10900 (SFU - IRMACS)
On Jacobians of dimension 2g that decompose into Jacobians of dimension g
room ASB 10900 (SFU - IRMACS)
Thu 23 Oct 2014, 3:30pm-4:30pm

Abstract

Let X be a genus 2g curve defined over an arbitrary field of characteristic not equal to 2 and let J(X) the Jacobian variety of X. We say that a Jacobian variety is decomposable if it is isogenous to a product of abelian varieties. The type of decomposition can by characterized by the type of kernel of the isogeny and the dimensions of the varieties in the product. We consider isogenies with kernel type (Z/2Z)g and products of dimension g Jacobian varieties. Additionally, we insist that the isogeny is polarized. In this talk we describe a family of (non-hyperelliptic) genus 2g curves whose Jacobians are decomposable in this way. We prove that all genus 4 curves whose Jacobian has this decomposition type are either in this family or arise from a different construction considered by Legendre. Joint work with Nils Bruin.
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Department of Mathematics, University of South Carolina
Fri 24 Oct 2014, 3:00pm
Department Colloquium
MATX 1100
A new asymptotic enumeration technique: the Lovasz Local Lemma
MATX 1100
Fri 24 Oct 2014, 3:00pm-4:00pm

Abstract

The lopsided version of the Lovasz Local Lemma gives asymptotically tight lower boundsfor a number of enumeration problems. In the configuration model matching upper bounds are available. In this way a number of asymptotic enumeration results, mostly due to Wormald and McKay, can be proved in an alternative way. A new result is asymptotic enumeration of graphs with respect to degree sequence and girth.  A classical probabilistic result of Paul Erdos showed the existence of graphs with arbitrary large girth and chromatic number. If the degree sequence satisfies some mild conditions, we show that almost all graphs with this degree sequence and prescribed girth have high chromatic number.
This is joint work with Lincoln Lu.

Note for Attendees

Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.
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