Mathematics Dept.
  Events
Dana C. Ernst, Angie Hodge & Andrew Schultz
Thu 1 Oct 2015, 10:30am
Math Education Research Reading
"Enhancing Proof Writing via Cross-Institutional Peer Review”
Thu 1 Oct 2015, 10:30am-11:30am

Abstract

 
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UBC
Fri 2 Oct 2015, 12:00pm
Graduate Student Seminar
Math 103
The continued fraction of Euler's number
Math 103
Fri 2 Oct 2015, 12:00pm-1:00pm

Abstract

 This will be a short talk on the derivation of the continued fraction of e = 2.718281828...

Note for Attendees

 Pizza and pop will be provided.
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UBC Math
Fri 2 Oct 2015, 3:00pm
Department Colloquium
MATX 1100
Bounding hard squares
MATX 1100
Fri 2 Oct 2015, 3:00pm-4:00pm

Abstract

Start labelling the vertices of the square grid with 0's and 1's with the condition that any pair of neighbouring vertices cannot both be labelled 1. If one considers the 1's to be the centres of small squares (rotated 45 degrees) then one has a picture of square-particles that cannot overlap. This problem of
"hard-squares" appears in different areas of mathematics - for example it has appeared separately as a lattice gas in statistical mechanics, as independent sets in combinatorics and as the golden-mean shift in symbolic dynamics.

A core question in this model is to quantify the number of legal configurations - the entropy. In this talk I will discuss the what is known about the entropy and describe our recent work finding rigorous and precise bounds for hard-squares and related problems.

This is work together with Yao-ban Chan.

Note for Attendees

Refreshments will be served in the MATH 125 lounge area at 2:45 p.m. before the colloquium.
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University of Washington
Mon 5 Oct 2015, 3:00pm
Algebraic Geometry Seminar
MATH 126
Projectivity of the moduli space of stable log-varieties
MATH 126
Mon 5 Oct 2015, 3:00pm-4:00pm

Abstract

 This is a report on joint work with Zsolt Patakfalvi. We prove a strengthening of Kollár's Ampleness Lemma and use it to prove that any proper coarse moduli space of stable log-varieties of general type is projective. We also confirm the Iitaka-Viehweg conjecture on the subadditivity of log-Kodaira dimension for fiber spaces whose general fiber is of log general type.

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Ben Krause
UBC/PIMS
Mon 5 Oct 2015, 3:00pm
Harmonic Analysis Seminar
Math Annex 1102
Discrete Analogues in Harmonic Analysis: Quadratic Carleson
Math Annex 1102
Mon 5 Oct 2015, 3:00pm-4:30pm

Abstract

Since the late eighties, when Bourgain proved his celebrated pointwise ergodic theorems, discrete analogues in harmonic analysis have come into vogue. Indeed, much work has been devoted to studying maximal functions and (maximal truncations of) singular integrals. The Carleson operator --  strictly more singular than either above operator -- is a natural operator to try adapt to the discrete setting: Eli Stein has been successful in "transferring" the continuous result to the discrete setting. In particular, he has established the L^2(\Z) boundedness of the discrete Carleson operator
\[ \sup_{\lambda} | \sum_{m \neq 0} f(n-m) e^{2\pi i \lambda m}/m |.\]
The purpose of this talk will be to study a discrete analogue of the quadratically modulated Carleson operator:
\[ \sup_{\lambda} | \sum_{m \neq 0} f(n-m) e^{2\pi i \lambda m^2}/m | \]
where \lambda ranges over certain subsets of (0,1].

This will be the first talk of the sequence, and very little background is required -- though the argument will eventually combine elements from analytic number theory, probability theory, and harmonic analysis.
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Anna Barry
Department of Mathematics, UBC
Tue 6 Oct 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Relative Equilibria with a Dominant Vortex
ESB 4133 (PIMS Lounge)
Tue 6 Oct 2015, 12:30pm-1:30pm

Abstract

In fluids, the presence of a dominant vortex has an organizing effect on the surrounding flow. We exploit this effect to simplify the stability problem for relative equilibria of (N+1) interacting point vortices, where N vortices have infinitesimal circulation and one vortex is strong in relation. Within this framework, existence and stability of equilibria reduces to characterizing critical points of a function defined on a circle. In the case that all vortices have circulation of the same sign, this function is potential-like, with minima corresponding to stable configurations and maxima and saddle points corresponding to unstable solutions. Surprisingly, typical stable configurations exhibit asymmetry.

Note for Attendees

Sushi lunch will be provided.
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University of Aveiro
Tue 6 Oct 2015, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
An Introduction to Convolutional codes
Math 126
Tue 6 Oct 2015, 2:00pm-3:00pm

Abstract

A follow-up talk on multidimensional convolutional codes will be given on Thursday, October 8.

Coding
 theory - theory of error correcting codes - is one of the most interesting and
applied parts of mathematics.Coding theory methods are often elegant applications of very basic concepts and methods of (abstract) algebra. IIn this talk we​ shall start by giving a brief general overview of this area before introducing the main topic of the talk, namely, convolutional codes

These codes are mathematically more involved than the standard block codes as they posses a very rich algebraic structure. In this context the data is considered as a sequence. Even though the data is split into blocks of a fixed rate as in block codes, the relative position of each block in the sequence is taken into account. The blocks are not encoded independently and previous nodes in the sequence have an effect over the next encoded node. Because of this, convolutional codes have memory. From a mathematical point of view they can be seen as F[x]-submodules of F[x]^n, where F is a finite field and F[x] is the ring of polynomials over F.

The aim of this talk is to introduce this powerful class of codes, their properties and their use in practice. We shall conclude by presenting some of the most fascinating open problems in the design of convolutional codes

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UBC
Tue 6 Oct 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
On type II singularity formulation of harmonic map flows
ESB 2012
Tue 6 Oct 2015, 3:30pm-4:30pm

Abstract

I will consider the following classical  harmonic map flow from a general two-dimensional domain D to S^2:

 u_t=\Delta u +|\nabla u|^2 u, u: D \to S^2

We develop a parabolic gluing method to construct finite time blow-up solutions of Type II in general domains. We show  that type II blow-up solutions with blow-up  rate

(T-t)/\log^2 (T-t)

is stable and generic in arbitrary domains (without any symmetry).  I will also discuss the construction of  multiple blow-ups, reverse bubbling, bubbling trees, bubbling at infinity. As a by-product we can perform new geometric surgeries. (Joint work with Manuel del Pino and Juan Davila.) 

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Abbas Mehrabian
UBC and SFU
Tue 6 Oct 2015, 4:00pm
Discrete Math Seminar
ESB 4127
Bounds for randomized rumour spreading protocols
ESB 4127
Tue 6 Oct 2015, 4:00pm-5:00pm

Abstract

Consider a social network modelled as a graph, with people and friendships represented by vertices and edges, respectively. Suppose that a person knows a piece of information, and as time passes, talks to other people and spreads it. How long it takes until everyone knows the rumour? The answer, which we call the "spread time", certainly depends on the graph's structure and how the rumour spreads. In this talk we discuss two well known randomized rumour spreading protocols (known as push&pull protocols) and survey the known results on their spread times on various graphs. 

Based on joint work with H. Acan, A. Collevecchio, and N. Wormald.
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University of British Columbia and Pacific institute for the Mathematical Sciences
Wed 7 Oct 2015, 3:00pm
Probability Seminar
ESB 2012
Restrictions of Brownian motion
ESB 2012
Wed 7 Oct 2015, 3:00pm-4:00pm

Abstract

It is classical that the zero set and the set of record times of a linear Brownian motion have Hausdorff dimension almost surely. Can we find a larger random subset on which a Brownian motion is monotone? Perhaps surprisingly, the answer is negative. We outline the short proof, which is an application of Kaufman's dimension doubling theorem for planar Brownian motion. This is a joint work with Yuval Peres.
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Camille Horbez
University of Utah
Wed 7 Oct 2015, 3:15pm
Topology and related seminars
ESB 4133
Subgroups of the automorphism group of a free product
ESB 4133
Wed 7 Oct 2015, 3:15pm-4:15pm

Abstract

I will discuss classification results for subgroups of Out(Fn) (analogous to Ivanov's classification of subgroups of mapping class groups of surfaces), and more generally of automorphism groups of free products. In particular, I will present a version of the Tits alternative for the automorphism group of a free product. This is partly joint work with Vincent Guirardel.
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Thu 8 Oct 2015, 10:30am
Math Education Research Reading
Math 126
History of Research in Mathematics Education
Math 126
Thu 8 Oct 2015, 10:30am-11:30am

Abstract

 
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Raquel Pinto
University of Aveiro
Thu 8 Oct 2015, 3:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102
Multidimensional Convolutional Codes
Math Annex 1102
Thu 8 Oct 2015, 3:00pm-4:00pm

Abstract


An introductory talk on one dimensional convolutional codes will be given on Tuesday, October 6.

Multidimensional 
(nD) convolutional codes generalize one dimensional (1D) convolutional codes and correspond to multidimensional systems widely studied in the systems theory literature. These codes have a practical potential in applications as they are very suitable to encode data recorded in n dimensions, e.g., pictures, videos, storage media, wireless applications, etc. However, in comparison to 1D convolutional codes, little is known in the area of nD convolutional codes and much more needs to be done to make it attractive for practical applications. From a mathematical point of view, these codes can be viewed as F[x_1,...,x_n]-submodules of F[x_1,...,x_n]^n, where F is a finite field and F[x_1,...,x_n] is the ring of polynomials in several variables over F. In this talk we present a construction of an nD convolutional code based on superregular matrices with excellent error-correcting capabilities.
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University of Auckland
Fri 9 Oct 2015, 3:00pm SPECIAL
Institute of Applied Mathematics
C680 HSBC Hall, Robson Square Campus (downtown)
The dynamics of aircraft as ground vehicles
C680 HSBC Hall, Robson Square Campus (downtown)
Fri 9 Oct 2015, 3:00pm-4:00pm

Abstract

Aircraft are designed to fly but also need to operate efficiently and safely as vehicles on the ground. The tricycle configuration of commercial aircraft presents challenges for manoeuvres, such as high-speed turns off a runway. The talk will present results of a collaboration with Airbus into the stability of ground manoeuvres, whose central idea is to employ tools from bifurcation analysis to relevant industry-validated aircraft models. Compared to standard extensive numerical simulations, this approach has been demonstrated to have potential efficiency benefits during the design stage. In particular, it allows for detailed studies of the nature of instabilities that need to be avoided in practice. As an example, we show that the sudden loss of lateral stability of a mid-size passenger aircraft turning on the ground is due to a canard phenomenon that arises due to a non-obvious slow-fast splitting.

This is joint work with Etienne Coetzee (Airbus), James Rankin (INRIA France), Mathieu Desroches (INRIA France) and Mark Lowenberg (University of Bristol).

Note for Attendees

Note this is the first of two talks at Robson Square campus. The second talk will be followed by a reception at 5:00. 
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University of Auckland
Fri 9 Oct 2015, 4:00pm SPECIAL
Institute of Applied Mathematics
C680 HSBC Hall, Robson Square Campus (downtown)
Shaken but not stirred: using mathematics in earthquakes
C680 HSBC Hall, Robson Square Campus (downtown)
Fri 9 Oct 2015, 4:00pm-5:00pm

Abstract

Predicting the behaviour of a structure when subjected to an earthquake is an important problem from Civil Engineering. Here, we consider a planar post-tensioned frame, which can be modelled as a two-degree-of-freedom system that is equivalent to the analytical model of a tied rocking block on an elastic foundation. The frame remains structurally sound as long as the tilt angle of the frame does not exceed a certain maximal angle. A standard approach to studying the dynamics would be to run simulations, where it is assumed that the earthquake is a pure sine wave with varying frequency and amplitude. Such a brute-force approach establishes a region in the frequency-amplitude plane for which the structural stability of the frame eventually fails. We propose a novel approach that calculates the failure region in a much more efficient way by determining the failure boundary directly. Our method is based on continuation of a suitable two-point boundary value problem. Our computations demonstrate that the failure boundary is only piecewise smooth and the results highlight further interesting details of how the dynamics is organised in the frequency-amplitude plane. 

Note for Attendees

Note this is the second of two talks at Robson Square campus. This talk will be followed by a reception at 5:00. 
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Davidson College
Tue 13 Oct 2015, 2:00pm
Number Theory Seminar
room IRMACS 10901 (SFU)
Oscillations in sums involving the Liouville function (note different day and time)
room IRMACS 10901 (SFU)
Tue 13 Oct 2015, 2:00pm-3:00pm

Abstract

The Liouville function λ(n) is the completely multiplicative arithmetic function defined by λ(p) = –1 for each prime pPólya investigated its summatory function L(x) = Σnλ(n), and showed for instance that the Riemann hypothesis would follow if L(x) never changed sign for large x. While it has been known since the work of Haselgrove in 1958 that L(x) changes sign infinitely often, oscillations in L(x) and related functions remain of interest in analytic number theory. We review some connections between oscillations in this function and its relatives with the Riemann hypothesis and other problems in number theory, and describe some recent work on this topic. In particular, we describe a method involving substantial computation that establishes new bounds on the magnitude of the oscillations of L(x). This is joint work with Tim Trudgian.
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Azahara de la Torre
Politechic University of Catalonia
Tue 13 Oct 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
On singular solutions for the fractional Yamabe problem
ESB 2012
Tue 13 Oct 2015, 3:30pm-4:30pm

Abstract

 Abstract: We construct some ODE solutions for the fractional Yamabe problem in conformal geometry. The fractional curvature, a generalization of the usual scalar curvature, is defined from the conformal fractional Laplacian, which is a non-local operator constructed on the conformal infinity of a conformally compact Einstein manifold.
These ODE solutions are a generalization of the usual Delaunay and, in particular, solve the fractional Yamabe problem
$$ (-\Delta)^\gamma u= c_{n, {\gamma}}u^{\frac{n+2\gamma}{n-2\gamma}}, u>0 \ \mbox{in} \ \r^n \backslash \{0\},$$
with an isolated singularity at the origin.
This is a fractional order ODE for which new tools need to be developed. The key of the proof is the computation of the fractional Laplacian in polar coordinates.
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Bert Guillou
University of Kentucky
Tue 13 Oct 2015, 4:00pm
Topology and related seminars
ESB 4133
The eta-local motivic sphere
ESB 4133
Tue 13 Oct 2015, 4:00pm-5:00pm

Abstract

The Hopf map eta is nilpotent in the stable homotopy groups of spheres. This is not so for the motivic Hopf map, considered as an element of the motivic stable homotopy groups of spheres. This suggests that the eta-local part of motivic stable homotopy theory is an interesting object of study. We will describe this for the base fields C and R.

Note for Attendees

Note different day and time.
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Université Paris Diderot
Wed 14 Oct 2015, 3:00pm
Probability Seminar
ESB 2012
Cutoff for non-backtracking random walks on sparse random graphs
ESB 2012
Wed 14 Oct 2015, 3:00pm-4:00pm

Abstract

A finite ergodic Markov chain exhibits cutoff if its distance to stationarity remains close to 1 over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Here we consider non-backtracking random walks on random graphs with a given degree sequence. Under a general sparsity condition, we establish the cutoff phenomenon, determine its precise window, and prove that the cutoff profile approaches a remarkably simple, universal shape. This is a joint work with Justin Salez (Paris-Diderot).
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Thu 15 Oct 2015, 10:30am
Math Education Research Reading
MATH 126
Clickers in the Large Classroom: Current Research and Best-Practice Tips
MATH 126
Thu 15 Oct 2015, 10:30am-11:30am

Abstract

 
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Ben Adcock
SFU
Thu 15 Oct 2015, 12:00pm
Mathematics of Information and Applications Seminar
ESB 4133 (PIMS Lounge)
Compressed sensing with local structure: theory, applications and benefits
ESB 4133 (PIMS Lounge)
Thu 15 Oct 2015, 12:00pm-1:00pm

Abstract

Compressed sensing concerns the recovery of signals and images from seemingly incomplete data sets. Introduced nearly a decade ago, it has since become an intensive area of research in applied mathematics, engineering and computer science. However, many practical problems in which compressed sensing is applied, e.g. imaging, are not fully explained by existing theory. In this talk I will present a new framework for compressed sensing that seeks to bridge this gap. This framework is based on replacing some standard principles of compressed sensing with new local notions; specifically, sparsity in levels, local coherence in levels and multilevel random subsampling. I will demonstrate a series of near-optimal recovery guarantees based on these local concepts that explains the effectiveness of compressed sensing in such applications. Moreover, this framework is not just useful in understanding existing compressed sensing approaches. In the final part of the talk I will demonstrate how leveraging local sparsity through appropriately-designed locally incoherent sensing matrices leads to substantially improved compressed sensing techniques in a range of other applications.
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UBC
Fri 16 Oct 2015, 12:00pm
Graduate Student Seminar
Math 103
A large subset of the real numbers avoiding nontrivial solutions to a linear equation
Math 103
Fri 16 Oct 2015, 12:00pm-1:00pm

Abstract

In 1998, Tamas Keleti constructed a subset of the reals of Hausdorff dimension 1 that does not contain 4 distinct points x_1, x_2, x_3, x_4 satisfying

x_2 - x_1 = x_4 - x_3.

I will describe this construction and some further directions that the construction can be taken.

Note for Attendees

 Pizza and pop will be provided.
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Colin B. Macdonald
UBC Mathematics
Fri 16 Oct 2015, 3:00pm
Department Colloquium
MATX 1100
Numerical Computation on Curved Surfaces
MATX 1100
Fri 16 Oct 2015, 3:00pm-4:00pm

Abstract

Despite the appearance sometimes given in textbooks, not all differential equations are posed on straight lines and rectangles. This talk will introduce some easy-to-use techniques for computing numerical solutions to partial differential equations (PDEs) posed on curved surfaces and other general domains.

I will show some applications in thin-film flows, reaction-diffusion equations, bulk-surface coupling, point clouds, and image processing.

The talk will also outline how a close encounter with instability improved our understanding and numerical analysis of these methods.
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University of Fribourg
Mon 19 Oct 2015, 3:00pm
Algebraic Geometry Seminar
MATH 126
Motivic classes of classifying stacks and their invariants
MATH 126
Mon 19 Oct 2015, 3:00pm-4:00pm

Abstract

After introducing the class of the classifying stack of a (finite) group, BG, in the Grothendieck ring of algebraic stacks, I will present certain cohomological invariants for a group - the Ekedahl invariants.

I am going to show that the class of BG is trivial if G is a finite subgroup of GL_3(k) or if G is a finite linear (or projective) reflection group. (k is a algebraically closed field of characteristic zero.) I will also show that the Ekedahl invariants of the discrete 5-Heisenberg group are trivial.

These results relate naturally to Noether's Problem and to its obstruction, the Bogomolov multiplier.

At the end of the talk, I will link these results to the study of the motivic classes of the quotient varieties V/G by showing that such classes and the classes of BG exhibit the same combinatorial structure. Therefore, despite the title and technical terminology I will aim at making the talk enjoyable also by the combinatorial community. 

(Partial joint work with Emanuele Delucchi.)
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Ben Krause
UBC/PIMS
Mon 19 Oct 2015, 3:00pm
Harmonic Analysis Seminar
Math Annex, 1102
Discrete Analogues in Harmonic Analysis: Quadratic Carleson, II
Math Annex, 1102
Mon 19 Oct 2015, 3:00pm-4:30pm

Abstract

 In the first talk in this lecture series, we introduced discrete analogues in harmonic analysis, and discussed Bourgain's celebrated polynomial ergodic theorem. In this second lecture in the series, we will apply Bourgain's approximation arguments in the study of the discrete quadratic Carleson operator,
\[ C_\Lambda f(n) := \sup_{\lambda \in \Lambda} | \sum_{m \neq 0} e(\lambda m^2)/m f(n-m) | \]
where $\Lambda \subset [0,1]$ is a set of modulation parameters, and $e(t) := e^{2\pi i t}$.
In particular, we will reduce matters to a multi-frequency maximal multiplier theorem, which we will study using three separate techniques:
  • Comparison to a multi-frequency multi-frequency maximal multiplier theorem involving truncations of the Hilbert transform;
  • A Fourier-analytic entropy/chaining argument; and
  • A TT* argument from the theory of oscillatory integrals.


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University of Toronto
Mon 19 Oct 2015, 4:15pm
Algebraic Geometry Seminar
MATH 126
Theta lifts and currents on Shimura varieties
MATH 126
Mon 19 Oct 2015, 4:15pm-5:15pm

Abstract

The Shimura varieties X attached to orthogonal and unitary groups come equipped with a large collection of so-called special cycles. Examples include Heegner divisors on modular curves and Hirzebruch-Zagier cycles on Hilbert modular surfaces. We will review work of Borcherds and Bruinier using regularised theta lifts for the pair (SL_2,O(V)) to construct Green currents for special divisors. Then we will explain how to construct other interesting currents on X using the dual pair (Sp_4,O(V)). We will show that one obtains currents in the image of the regulator map of a certain motivic complex of X. Finally, we will describe how an argument using the Siegel-Weil formula allows to relate the values of these currents to the product of a special value of an L-function and a period on a certain subgroup of Sp_4.
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PIMS/University de Tours
Wed 21 Oct 2015, 3:00pm
Probability Seminar
ESB 2012
Discrete harmonic functions in the quadrant
ESB 2012
Wed 21 Oct 2015, 3:00pm-4:00pm

Abstract

In this talk we shall be interested in discrete harmonic functions in cones (in particular, in the quarter plane). The generating function of these harmonic functions satisfies a functional equation (closed to a well-known functional equation that appears in the context of enumeration of confined walks in combinatorics). We shall show the link between these harmonic functions and a one-parameter family of conformal mappings. One of the motivations to that study is to condition (in the sense of Doob) random walks never to leave cones.
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Kyle Ormsby
Reed College
Wed 21 Oct 2015, 3:15pm
Topology and related seminars
ESB 4133
Tensor triangular geometry of the stable motivic homotopy category
ESB 4133
Wed 21 Oct 2015, 3:15pm-4:15pm

Abstract

In Balmer's framework of tensor triangular geometry, the prime thick tensor ideals in a tensor triangulated category C form a space which admits a continuous map to the Zariski spectrum Spec^h(End_u(1)) of homogeneous prime ideals in the graded endomorphism ring of the unit object.  (Here the grading is induced by an element u of the Picard group of C.)  If C is the stable motivic homotopy category and u is the punctured affine line, then this endomorphism ring is the Milnor-Witt K-theory ring of the base field.  I will describe work by my student, Riley Thornton, which completely determines the homogeneous Zariski spectrum of Milnor-Witt K-theory in terms of the orderings on the base field.  I will then comment on work in progress which uses the structure of this spectrum to study the thick subcategories of the stable motivic homotopy category.
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Thu 22 Oct 2015, 10:30am
Math Education Research Reading
Math 126
"Beyond Plug and Chug: an Analysis of Calculus I Homework"
Math 126
Thu 22 Oct 2015, 10:30am-11:30am

Abstract

 
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SFU
Thu 22 Oct 2015, 3:30pm
Number Theory Seminar
room MATH 126
An arithmetic graph invariant with applications in quantum field theory
room MATH 126
Thu 22 Oct 2015, 3:30pm-4:30pm

Abstract

I will give an overview of things we know about c2 invariant of a graph. This is an invariant investigated principally by Brown and Schnetz which comes from counting points on the hypersurface defined by the Kirchhoff polynomial of a graph. This invariant predicts many properties of the Feynman integral of the graph. It connects with deep things like modular forms and motives. Many computations involving it come down to playing around with polynomials defined from the graph and so its also combinatorial. The fun and power of it come from the interplay of all three of these things.
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Ben Krause
UBC/PIMS
Mon 26 Oct 2015, 3:00pm
Harmonic Analysis Seminar
Math Annex 1102
Discrete Analogues in Harmonic Analysis: Quadratic Carleson, III
Math Annex 1102
Mon 26 Oct 2015, 3:00pm-4:30pm

Abstract

In the second talk in the series on the discrete quadratic Carleson operators,
\[ C_\Lambda f(n) := \sup_{\lambda \in \Lambda} | \sum_{m \neq 0} e^{2\pi i \lambda m^2}/m f(n-m), \Lambda \subset [0,1] \]
we reduced matters to a multi-frequency maximal multiplier theorem.
In this third talk we will prove that the operator norm of the multi-frequency maximal multiplier is slowly growing in the number of distinguished frequencies. We use three separate techniques to do so; the highlight of our approach is a novel entropy argument.

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UBC
Mon 26 Oct 2015, 3:00pm
Algebraic Geometry Seminar
MATH 126
Non-finitely generated Cox rings
MATH 126
Mon 26 Oct 2015, 3:00pm-4:00pm

Abstract

Cox rings of algebraic varieties were defined by Hu and Keel in relation to the minimal model program. The main question in the theory is to determine if the Cox ring of a variety is finitely generated. Such varieties are called Mori Dream Spaces. In this talk I will discuss examples of varieties that are not Mori Dream Spaces. These include toric surfaces blown up at a point and the moduli spaces of rational curves with n points. This is a joint work with Jose Gonzalez.
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Department of Civil Engineering, UBC
Tue 27 Oct 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
An earthquake early warning network for BC - how does it work?
ESB 4133 (PIMS Lounge)
Tue 27 Oct 2015, 12:30pm-1:30pm

Abstract

This talks will describe the concept of earthquake early warning and will include a description of the different methods and approaches used to detect earthquake shaking.  An overview of the work being done in BC to establish and implement an EEW network for BC will be presented.  This includes a description of the hardware and software that has been, and is being, developed.  The future directions of the network will be presented and the opportunities for collaboration with various research groups at UBC will be discussed.

Note for Attendees

Sushi lunch and mini juices will be provided.
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University of Tennessee, Knoxville
Tue 27 Oct 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Gradient estimates and global existence of smooth solutions to a cross-diffusion system
ESB 2012
Tue 27 Oct 2015, 3:30pm-4:30pm

Abstract

We investigate the global time existence of smooth solutions for the Shigesada-Kawasaki-Teramoto system of cross-diffusion equations of two competing species in population dynamics. If there are self-diffusion in one species and no cross-diffusion in the other, we show that the system has a unique smooth solution for all time in bounded domains of any dimension. We obtain this result by deriving global W^{1,p}-estimates of Calder\'{o}n-Zygmund type  for a class of nonlinear reaction-diffusion equations with self-diffusion. These estimates are achieved by employing Caffarelli-Peral perturbation technique together with a new two-parameter scaling argument.

The talk is based on the joint work with L. Hoang (Texas Tech) and T. Nguyen (U. of Akron).


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Abbas Mehrabian
UBC and SFU
Tue 27 Oct 2015, 4:00pm
Discrete Math Seminar
ESB 4127
Cops and a Fast Robber on Planar and Random Graphs
ESB 4127
Tue 27 Oct 2015, 4:00pm-5:00pm

Abstract

 We study a variant of the Cops and Robber game, in which the robber has unbounded speed, i.e., can take any path from her vertex in her turn, but she is not allowed to pass through a vertex occupied by a cop.  Let c(G) denote the number of cops needed to capture the robber in a graph G, and let tw(G) denote the treewidth of G.  We show that if G is planar then c(G) = Theta(tw(G)), and there is a polynomial-time constant-factor approximation algorithm for computing c(G).  We also determine, up to constant factors, the value of c(G) of the random graph G(n,p) for all admissible values of p, and show that when the average degree goes to infinity, c(G) is typically asymptotic to the domination number.  

This is joint work with Noga Alon.
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Cornell University
Wed 28 Oct 2015, 3:00pm
Probability Seminar
ESB 2012
Circles in the Sand
ESB 2012
Wed 28 Oct 2015, 3:00pm-4:00pm

Abstract

I will describe the role played by an Apollonian circle packing in the scaling limit of the abelian sandpile on the square grid Z^2. The sandpile solves a certain integer optimization problem. Associated to each circle in the packing is a locally optimal solution to that problem. Each locally optimal solution can be described by an infinite periodic pattern of sand, and the patterns associated to any four mutually tangent circles obey an analogue of the Descartes Circle Theorem. Joint work with Wesley Pegden and Charles Smart.
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Omar Antolin Camarena
UBC Math
Wed 28 Oct 2015, 3:15pm
Topology and related seminars
ESB 4133
A simple universal property of Thom ring spectra
ESB 4133
Wed 28 Oct 2015, 3:15pm-4:15pm

Abstract

A stable spherical fibration is classified by a map X → BGL₁(S) and Lewis showed that if this map is an infinite loop map or an n-fold loop map then the Thom spectrum is an E_∞- or E_n-ring spectrum, respectively. Ando, Blumberg, Hopkins, Gepner and Rezk introduced a new approach to Thom spectra using the language of ∞-categories. Using their approach, we will explain how to apply some simple (∞-)category theory to study multiplicative structures on Thom spectra, proving a generalization of Lewis's theorem and moreover characterizing the ring structure by a universal property. As an application I'll discuss a new (slightly simpler) proof of a remarkable theorem of Mahowald's realizing the Eilenberg-MacLane spectrum HF₂ as a Thom spectrum of a double loop map.
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Thu 29 Oct 2015, 10:30am
Math Education Research Reading
Math126
"Socioeconomic Influence on Mathematical Achievement: What Is Visible and What Is Neglected"
Math126
Thu 29 Oct 2015, 10:30am-11:30am

Abstract

 
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Carleton University
Thu 29 Oct 2015, 3:00pm
Number Theory Seminar
room MATH 126
A method for computing Arthur-packets at Archimedean places
room MATH 126
Thu 29 Oct 2015, 3:00pm-4:00pm

Abstract

Let G be a connected reductive algebraic group defined over a number field. The harmonic analysis of the adelic points of G leads to a decomposition of the regular representation into automorphic representations. The irreducible subrepresentations in this decomposition form the so-called discrete spectrum. When G=GLn the discrete spectrum has a nice description. Langlands' principle of functoriality suggests that the discrete spectrum of other groups might be described in terms of the discrete spectrum of GLn. Arthur has recently provided such a description for symplectic and special orthogonal groups in terms of sets of representations called A(rthur)-packets. The structure of A-packets is not well understood, and relies in part on their local analogues. We will outline a method for computing A-packets for real groups.
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Emory University
Thu 29 Oct 2015, 4:00pm
Number Theory Seminar
room MATH 126
Reciprocity obstructions to Hasse principle over function fields of p-adic curves
room MATH 126
Thu 29 Oct 2015, 4:00pm-5:00pm

Abstract

A variety X over a number field k is said to satisfy Hasse principle of it has a rational point provided it has a rational point over completions of k at all its places. Manin defined an obstruction in terms of the Brauer group to detect the failure of Hasse principle for varieties over number fields which is referred to as the Brauer-Manin obstruction. This obstruction is the only obstruction to Hasse principle for torsors under connected linear algebraic groups over k. We shall explain a reciprocity obstruction to Hasse principle for varieties over function fields of p-adic curves. This obstruction can be used to produce examples of principal homogeneous spaces under tori which fail Hasse principle over function fields of p-adic curves.
 
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UBC
Fri 30 Oct 2015, 12:00pm
Graduate Student Seminar
Math 103
Spheres of spheres over spheres: An analysis of the group structure of the n-sphere, S^n and the Hopf fibration.
Math 103
Fri 30 Oct 2015, 12:00pm-1:00pm

Abstract

 Do you like spheres? If not, you are wrong, and probably won't like this talk. To the remaining reasonable people out there hold on to your socks. It is an elementary fact that the 0-sphere S^0=\{\pm 1\} is the group \mathbb{Z}_2 and the circle S^1 is also the group e^{i\theta}. Is that just by chance, can all groups be given a group structure? If not what makes the ones that can so special? We will analyse which spheres have this property (turns out only 3.5ish do) and how to find the group structure when they do.

The question now becomes, what can we say about the spheres that can't be groups? Can we exploit the symmetries of S^n and the sphere groups above to salvage some geometric structure? To answer these questions we will begin by give a very elementary introduction to fibre bundles (emphasis on the ``very''), and discuss how we can think of higher order spheres as a bunch of copies (ie. fibres) of sphere groups by constructing the Hopf fibration. Time permitting, we will give an application of this abstract jargon to help visualize the spin \frac{1}{2}-system in quantum mechanics and introduce the bloch sphere.

This is meant to be very elementary, if you understood the first paragraph, you will understand this talk. The goal will be to focus on intuition and avoid technical details like the plague.

Note for Attendees

 Pizza and pop will be provided.
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Emory University
Fri 30 Oct 2015, 3:00pm
Department Colloquium
ESB 2012
PIMS/UBC Distinguished Colloquium: Local-global principles for quadratic forms
ESB 2012
Fri 30 Oct 2015, 3:00pm-4:00pm

Abstract

The classical theorem of Hasse-Minkowski asserts that a quadratic form over a number field represents zero nontrivially provided it represents zero nontrivially over its completions at all its places. We discuss analogous local global principles over function fields of p-adic curves. Such local-global principles in the general setting for homogeneous spaces have implications to the understanding of the arithmetic of these fields.
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