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 Events
University of California at Irvine
Tue 4 Oct 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
On the first eigenvalue estimate for sub-Laplacian and Kohn Laplacian and Rigidity Theorems on pseudo-Hermitian CR manifolds
ESB 2012
Tue 4 Oct 2016, 3:30pm-4:30pm

Abstract

 In this talk, I will present  a CR-version of Lichnerowicz--Obata type theorem in a closed pseudo-Hermitian CR manifolds. It includes the lower bound estimates for the first positive eigenvalue for the both sub-Laplacian and Kohn Laplacian. I will also provide Obata type theorem associated to the sub-Laplacian and Kohn Laplacian on a closed pseudo-Hermitian manifold. As an application, we give some rigidity theorem when lower bound of eigenvalue is achieved. This is based on a joint work with X. Wang and a joint work with Duong N. Son and Wang. I will also talk about some ongoing work in this topic.
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Santiago Salazar
UBC
Tue 4 Oct 2016, 4:00pm
Discrete Math Seminar
ESB 4127
Forbidden Berge hypergraphs
ESB 4127
Tue 4 Oct 2016, 4:00pm-5:00pm

Abstract

 Given two matrices A,B we say that A is a Berge hypergraph of B if there is a submatrix of B, say matrix D, and a row and column permutation of A, say matrix C, so that C<=D. Define Av(m,F) to be the set of all m-rowed (0,1)-matrices with no repeated columns and no Berge hypergraph F. Define Bh(m,F) to be the maximum, over all matrices A in Av(m,F), of the number of columns of A. We are interested in determining the asymptotic growth of Bh(m,F) for specific F. We show some techniques we can use to this end and mention the general results determined for F with 5 or fewer rows. We also show that if F is the vertex-edge incidence matrix of a tree then bh(m,F) has a linear bound. When F is the vertex-edge (s+t)x(st) incidence matrix of the bipartite graph K_{s,t} we show that finding Bh(m,F) relates to determining ex(m,K_r,K_{s,t} ), the maximum number of complete subgraphs K_r in a m-vertex graph avoiding K_{s,t} as a subgraph. Recent papers by Alon and others have solved some cases.
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Cindy Greenwood
UBC
Wed 5 Oct 2016, 1:45pm
Mathematical Biology Seminar
PIMS (ESB 4th floor)
Hidden Patterns Revealed by Noise: semi-arid vegetation patterns
PIMS (ESB 4th floor)
Wed 5 Oct 2016, 1:45pm-2:45pm

Abstract

A deterministic model may sometimes seem to be a good description of the dynamics of an observed system but may have a long-term stable constant limit, whereas observations of the system itself show a noisy pattern. An example is semi-arid vegetation patterns. Adding noise to the model may well reveal the pattern. In this talk I show some photos, talk about some math, and show some simulations. This is not a magic show.
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UBC Computer Science and PIMS
Wed 5 Oct 2016, 3:00pm
Probability Seminar
ESB 2012
On longest paths and diameter in random Apollonian networks
ESB 2012
Wed 5 Oct 2016, 3:00pm-4:00pm

Abstract

Consider the following iterative construction of a random planar triangulation. Start with a triangle embedded in the plane. In each step, choose a bounded face uniformly at random, add a vertex inside that face and join it to the vertices of the face. After n – 3 steps, we obtain a random triangulated plane graph with n vertices, which is called a Random Apollonian Network (RAN). See http://www.math.cmu.edu/~ctsourak/ran.html for an example.

We prove that the diameter of a RAN is asymptotic to c log(n) in probability, where c ≈ 1.668 is the solution of an explicit equation. The proof adapts a technique of Broutin and Devroye for estimating the height of random trees.

We also prove that there exists a fixed s<1, such that eventually every self-avoiding walk in this graph has length less than n^s, which verifies a conjecture of Cooper and Frieze. Using a similar technique, we show that if r < d are fixed constants, then every r-ary subtree of a random d-ary recursive tree on n vertices has less than n^b vertices, for some b=b(d,r)<1.

Based on joint work with A. Collevecchio, E. Ebrahimzadeh, L. Farczadi, P. Gao, C. Sato, N. Wormald, and J. Zung.
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Western Washington University
Wed 5 Oct 2016, 3:00pm
Harmonic Analysis Seminar
MATH 126
On probabilistic Strichartz estimates for the NLS
MATH 126
Wed 5 Oct 2016, 3:00pm-4:00pm

Abstract

We will begin by briefly discussing the non-linear Schroedinger (NLS) equation and the corresponding classical Strichartz estimates. We will then introduce a so-called Wiener randomization of initial data and indicate how it leads to an improvement of the classical Strichartz estimates. As a toy application, we will show how, in contrast with the deterministic case, the energy-critical cubic NLS in four dimensions is almost surely well-posed with respect to randomized initial data below the energy space. This is a joint work with Tadahiro Oh (University of Edinburgh) and Oana Pocovnicu (Heriot-Watt University).
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University of Southern California
Wed 5 Oct 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
A new proof of the decomposition theorem
ESB 4133 (PIMS Lounge)
Wed 5 Oct 2016, 3:15pm-4:15pm

Abstract

In this talk, we will discuss a new proof of the decomposition theorem of Beilinson, Bernstein, Deligne and Gabber for semi-simple perverse sheaves of geometric origin on complex algebraic varieties. This proof follows from rather formal considerations of higher algebra, stable motivic homotopy theory and Grothendieck's six functors, avoiding both the positive-characteristic methods of the original proof, and the delicate analysis of degenerations of mixed Hodge structures involved in M. Saito's proof.
 
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Laure Saint-Raymond
Harvard University, ENS, France
Thu 6 Oct 2016, 2:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 4127
Fluid limits of systems of particles
ESB 4127
Thu 6 Oct 2016, 2:00pm-3:00pm

Abstract


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Laure Saint-Raymond
Harvard University, ENS
Fri 7 Oct 2016, 3:00pm SPECIAL
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium--Propagation of chaos and irreversibility in gas dynamics
ESB 2012
Fri 7 Oct 2016, 3:00pm-4:00pm

Abstract

 

Note for Attendees

Refreshments (A light reception) are served in ESB 4133 from 2:30pm-3:00pm before the colloquium.
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Jessica Bosch
Department of Computer Science, UBC
Tue 11 Oct 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge) Rescheduled to Oct 11th.
Fast Iterative Solvers for Cahn-Hilliard Problems
ESB 4133 (PIMS Lounge) Rescheduled to Oct 11th.
Tue 11 Oct 2016, 12:30pm-1:30pm

Abstract

The Cahn-Hilliard equation models the motion of interfaces between several phases. The underlying energy functional includes a potential for which different types were proposed in the literature. We consider smooth and nonsmooth potentials with a focus on the latter. In the nonsmooth case, we apply a function space-based algorithm, which combines a Moreau-Yosida regularization technique with a semismooth Newton method. We apply classical finite element methods to discretize the problems in space. At the heart of our method lies the solution of large and sparse fully discrete systems of linear equations. Block preconditioners using effective Schur complement approximations are presented. For the smooth systems, we derive optimal preconditioners, which are proven to be robust with respect to crucial model parameters. Further, we prove that the use of the same preconditioners give poor approximations for the nonsmooth formulations. The preconditioners we present for the nonsmooth problems incorporate the regularization terms. Extensive numerical experiments show an outstanding behavior of our developed preconditioners. Our strategy applies to different Cahn-Hilliard problems including phase separation and coarsening processes, image inpainting, and two-phase flows. 
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Tobias Huxol
UBC
Tue 11 Oct 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Refined Asymptotics of the Teichm\"uller harmonic map flow
ESB 2012
Tue 11 Oct 2016, 3:30pm-4:30pm

Abstract

 The Teichm\"uller harmonic map flow is a gradient flow for the harmonic map energy of maps from a closed surface to a general closed Riemannian target manifold of any dimension, where both the map and the domain metric are allowed to evolve. It was introduced by M. Rupflin and P. Topping in 2012. The objective of the flow is to find branched minimal immersions on a given surface. We will give some background on the flow and then describe some recent work. In particular we show that if the flow exists for all times then in a certain sense the maps (sub-)converge to a collection of branched minimal immersions with no loss of energy (even when allowing for degeneration of the metric at infinity). We also construct an example of a smooth flow where the image of the limit maps is disconnected. This is joint work with M. Rupflin and P. Topping.
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UBC Math
Wed 12 Oct 2016, 3:00pm
Probability Seminar
ESB 2012
Voronoi cells in random graphs
ESB 2012
Wed 12 Oct 2016, 3:00pm-4:00pm

Abstract

 The Volumes of voronoi cells in random trees have a surprisingly simple law.  I will present a proof of this and related conjectures about the Brownian sphere.  Joint with Louigi Addario-Berry, Christina Goldschmidt, Guillaume Chapuy, and Eric Fusy.
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UBC
Wed 12 Oct 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Free actions by elementary abelian 2-groups
ESB 4133 (PIMS Lounge)
Wed 12 Oct 2016, 3:15pm-4:15pm

Abstract

Carlsson conjectured that if a finite complex admits a free action by an elementary abelian p-group of rank n, then the sum of its mod-p Betti numbers is at least 2^n. For the prime p=2, he reduced the conjecture to an algebraic problem which he solved for low n. In this talk, we will retrace Carlsson's journey through homological and commutative algebra. The following week, I will report on joint work in progress with Jeremiah Heller with the goal of extending Carlsson's methods to all primes.
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Prof. Joseph Anthony
Clinical Professor, Faculty of Medicine (on secondment to the LTE Renenwal Project)
Thu 13 Oct 2016, 12:30pm SPECIAL
Lunch Series on Teaching & Learning
MATH 126
What should the "new Connect" do?
MATH 126
Thu 13 Oct 2016, 12:30pm-1:30pm

Abstract

The end of UBC's current license with Blackboard Learn (badged locally as Connect) is approaching, and we need to assess future options for the application that sits at the core of our Learning Technology ecosystem.

We understand that the technology provided by Connect has not been satisfactory for faculty in the Mathematics Department. We'd like to hear about your needs, in order that these might inform the selection of the new LMS tool.
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Anne-Marie Aubert
Jussieu
Thu 13 Oct 2016, 3:30pm
Number Theory Seminar
ESB 4127
Classification of enhanced Langlands parameters for p-adic groups
ESB 4127
Thu 13 Oct 2016, 3:30pm-5:15pm

Abstract

We will start by introducing Langlands parameters and their enhanced versions. Then we will explain how to mirror the expected classification of  irreducible smooth representations of p-adic groups into a classification of corresponding  enhanced Langlands parameters. We will illustrate our construction with simple examples. It is joint work with Ahmed Moussaoui and Maarten Solleveld.
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Frank Sotille
TAMU
Thu 13 Oct 2016, 4:00pm
Discrete Math Seminar
Math 126
Murnaghan-Nakayama Rules in Schubert Calculus
Math 126
Thu 13 Oct 2016, 4:00pm-5:00pm

Abstract

 The Murnaghan-Nakayama  rule expresses  the product  of a
Schur function with a Newton power sum in the basis of Schur
functions.   As  the  power  sums generate  the  algebra  of
symmetric  functions,  the  Murnaghan-Nakayama  rule  is  as
fundamental as  the Pieri rule.  Interesting,  the resulting
formulas from the  Murnaghan-Nakayama rule are significantly
more  compact  than  those  from  the  Pieri  formula.   In
geometry,   a   Murnaghan-Nakayama  formula   computes   the
intersection  of Schubert  cycles with  tautological classes
coming from the Chern character.

In this talk, I will  discuss some background, and then some
recent    work    with    Andrew    Morrison    establishing
Murnaghan-Nakayama  rules for  Schubert polynomials  and for
the quantum  cohomology of the Grassmannian.   The results I
discuss are contained in the preprint arXiv:1507.06569.
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UBC Math
Fri 14 Oct 2016, 3:00pm
Department Colloquium
Math Annex 1100
Quantum Unique Ergodicity
Math Annex 1100
Fri 14 Oct 2016, 3:00pm-4:00pm

Abstract

I will survey the equidistribution problem for eigenfunctions of the Laplace operator, especially from the point of view of eigenfunction bounds. For the case of locally symmetric spaces I will discuss positive results for exact eigenfunctions (especially joint work with Anantharaman) and negative results for approximate eigenfunctions (joint work with Eswarathasan).

Note for Attendees

Refreshments will be served in MATH 125 at 2:45pm before the colloquium.
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UBC
Mon 17 Oct 2016, 3:00pm
Harmonic Analysis Seminar
MATH 126
Large Sets Avoiding Patterns
MATH 126
Mon 17 Oct 2016, 3:00pm-4:00pm

Abstract

 
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University of Michigan, Ann Arbor
Mon 17 Oct 2016, 3:00pm
Algebraic Geometry Seminar
MATX 1102
Noncommutative resolutions of singularities and the McKay correspondence
MATX 1102
Mon 17 Oct 2016, 3:00pm-4:00pm

Abstract

Motivated by algebraic geometry, one studies non-commutative analogs of resolutions of singularities. In short, a non-commutative resolution (=NCR) of a commutative ring R is an endomorphism ring of a certain R-module of finite global dimension. However, it is not clear how to construct non-commutative resolutions in general and which structure they have. The most prominent example of NCRs comes from the classical McKay correspondence that relates the geometry of so-called Kleinian surface singularities with the representation theory of finite subgroups of SL(2,\mathbb{C}). 

In this talk we will first review this fascinating result, exhibiting the connection to the ubiquitious Coxeter-Dynkin diagrams. Moreover, we will comment on an algebraic version of the correspondence, due to Maurice Auslander.

This leads to joint work in progress with Ragnar Buchweitz and Colin Ingalls about a version of the McKay correspondence when G in GL(n,\mathbb{C}) is a finite group generated by reflections: The group G acts linearly on the polynomial ring S in n variables over \mathbb{C}. When G is generated by reflections, then the discriminant D of the group action of G on S is a hypersurface with a singular locus of codimension 1. We give a natural construction of a NCR of the coordinate ring of D as a quotient of the skew group ring A=S*G. We will explain this construction, which gives a new view on Knörrer's periodicity theorem for matrix factorizations and allows to extend Auslander's theorem to reflection groups.

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UBC
Mon 17 Oct 2016, 3:00pm
Number Theory Seminar
ESB 4127
Sums of cubes, Heegner points, and p-adic L-functions
ESB 4127
Mon 17 Oct 2016, 3:00pm-5:00pm

Abstract

"Which numbers (and in particular, which primes) are sums of two rational cubes" is a classical and still-not-entirely-solved Diophantine problem. I'll talk about how it turns into a problem about rational points on elliptic curves, and how it can then be attacked using the modern machinery of the arithmetic of elliptic curves. In particular, proving that certain primes can be written as a sum of two cubes can be accomplished by constructing a Heegner-type point and proving it's nonzero. This is a subtle question and has been carried out in different ways by Elkies and by Dasgupta-Voight. My work (in process) gives a new method to carry this out, based on a new construction I've given of a certain type of anticyclotomic p-adic L-function.

Following the new format for the number theory seminar, this talk will consist of two 45-minute parts. The first 45 minutes will be expository and is intended to be accessible for graduate students in number theory. There will be a short break (when people are welcome to leave), and the second 45 minutes will be at a higher level.

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Saikat Mazumdar
UBC
Tue 18 Oct 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Higher order elliptic problems with critical sobolev growth on a compact riemannian manifold: Best constants and existence
ESB 2012
Tue 18 Oct 2016, 3:30pm-4:30pm

Abstract

We investigate the existence of solutions to a nonlinear elliptic problem involving the critical Sobolev exponent for a Polyharmomic operator on a Riemannian manifold M. We first show that the best constant of the Sobolev embedding on a manifold can be chosen as close as one wants to the Euclidean one, and as a consequence derive the existence of minimizers when the energy functional goes below a quantified threshold. Next, higher energy solutions are obtained by Coron's topological method, provided that the minimizing solution does not exist and the manifold satisfies a certain topological assumption. To perform the topological argument, we obtain a decomposition of Palais-Smale sequences as a sum of bubbles and adapt Lions's concentration-compactness lemma.
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Gizem Karaali
Pomona College
Tue 18 Oct 2016, 4:00pm
Discrete Math Seminar
ESB 4127
Supercharacters and their superpowers
ESB 4127
Tue 18 Oct 2016, 4:00pm-5:00pm

Abstract

Supercharacter theory, a generalization of character theory, was developed originally by Carlos Andre and then picked up and studied more extensively by Persi Diaconis and I. M. Isaacs. This new development in finite group representation theory has spurred much exciting work, leading to a range of results in algebraic combinatorics and number theory. I will begin at the (very) beginning, so no prior experience in supercharacter theory is required. 
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Dhananjay Bhaskar
UBC
Wed 19 Oct 2016, 1:45pm
Mathematical Biology Seminar
PIMS (ESB 4th floor)
A Machine Learning Approach to Morphology Based Cell Classification
PIMS (ESB 4th floor)
Wed 19 Oct 2016, 1:45pm-2:45pm

Abstract

Individual cells regulate their morphology in response to environmental cues, selective pressures and signalling. The precise mechanism(s) through which cells control their shape is not well understood. Studies have shown that cell morphology has important implications for nutrient uptake, motility, proliferation, etc. For example, a change in bacterial cell diameter of 0.2 μm can change the energy required for chemotaxis by a factor of 10^5. Automatic classification and counting can facilitate a systematic investigation of cell morphology. Furthermore, it is a useful tool for diagnosis of diseases like leukemia that are characterized by cell shape deformation. 
 
In this talk, I will describe techniques for image segmentation and feature extraction that we use to build a descriptor of cell shape. This descriptor is used to classify cells using unsupervised learning (PCA, hierarchical clustering) methods. I will briefly discuss the advantages and limitations of supervised learning (deep neural networks, convolutional neural networks) methods.
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University of Washington
Wed 19 Oct 2016, 3:00pm
Probability Seminar
ESB 2012
Extremal conformal metrics, spectral geometry, and distributional limits of graphs
ESB 2012
Wed 19 Oct 2016, 3:00pm-4:00pm

Abstract

I will talk about an intrinsic approach to uniformization of a graph's geometry based on extremal discrete metrics.  This method allows one to generalize known results about planar graphs that rely heavily on the theory of circle packings, and to obtain new information even for well-studied models of planar graphs like the uniform infinite triangulation (UIPT) and quadrangulation (UIPQ).
 
It yields a short proof of Benjamini and Schramm's result that a distributional limit of bounded-degree planar graphs is almost surely recurrent.  The same argument resolves a 2001 conjecture of those authors since it works also for H-minor-free graphs (and, in fact, a substantial generalization known as region intersection graphs).
 
Gurel-Gurevich and Nachmias recently solved a central open problem by showing that UIPT and UIPQ are almost surely recurrent.  By combining extremal discrete metrics with methods from spectral geometry, I will present a new proof of this fact that also gives explicit control on divergence of the Green function.  If g(x, T) denotes the number of returns to the root at time T, we show that almost surely (over the choice of the random rooted graph), g(x,T) grows asymptotically at least as fast as log log T.  This is a consequence of a general result that holds for any distributional limit of H-minor-free graphs and provides lower bounds on return probabilities based on the tails of the degree distribution of the root.
 
Finally, I will discuss extensions to general graphs and, in particular, give a characterization of the almost sure spectral dimension of a distributional limit in terms of the "conformal growth rate" of any sequence that approaches the limit graph.  This has consequences for graphs that can be sphere-packed in R^d for d > 2.
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UBC
Wed 19 Oct 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Free actions by elementary abelian p-groups
ESB 4133 (PIMS Lounge)
Wed 19 Oct 2016, 3:15pm-4:15pm

Abstract

Carlsson conjectured that if a finite complex admits a free action by an elementary abelian p-group of rank n, then the sum of its mod-p Betti numbers is at least 2^n. For the prime p=2, he reduced the conjecture to an algebraic problem which he solved for low n. In this talk, I will report on joint work in progress with Jeremiah Heller with the goal of extending Carlsson's methods to all primes. The crucial ingredient is a new notion of Koszul p-complexes.
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UBC Math
Fri 21 Oct 2016, 3:00pm
Department Colloquium
Math Annex 1100
Numerical modelling and high performance computing of particle-laden flows
Math Annex 1100
Fri 21 Oct 2016, 3:00pm-4:00pm

Abstract

Particle-laden flows are ubiquitous in environmental, geophysical and engineering processes. The intricate dynamics of these two-phase flows is governed by momentum transfer between the continuous fluid phase and the dispersed particulate phase. In this talk, I will suggest a multi-scale modelling framework for particle-laden flows and address mathematical and computational issues related to the numerical simulation of this type of flow. Based on various simulation results, I will present what can already be achieved with existing numerical models as well as the next stages in the development of faster and more accurate solution methods as e.g. fast Navier-Stokes solvers on cartesian grids, Adaptive Mesh Refinement or highly scalable numerical tools.

Note for Attendees

Refreshments will be served in MATH 125 at 2:45pm before the colloquium.
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Alessandro Marinelli
UBC
Mon 24 Oct 2016, 3:00pm
Harmonic Analysis Seminar
Math 126
(p,q)-strong unboundedness for the maximal directional Hilbert transform in dimension n
Math 126
Mon 24 Oct 2016, 3:00pm-4:00pm

Abstract

In 2007 G.A.Karagulyan proved that the maximal directional Hilbert transform over a set U of directions in the plane cannot be extended to a (2,q)-strongly bounded operator for any q in the range 1 ≤ q < +∞. In this talk, I will describe my proof of the generalization of this result and show that, for any 1 < p ≤ 2, any 1 ≤ q < +∞ and any dimension n ≥ 2, the maximal directional Hilbert transform over an infinite set of directions in IR^n, cannot be extended to a (p,q)-strongly bounded operator.
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UBC
Mon 24 Oct 2016, 3:00pm
Algebraic Geometry Seminar
MATX 1102
T-structures on coherent sheaves and categorical actions
MATX 1102
Mon 24 Oct 2016, 3:00pm-4:00pm

Abstract

I will review the notion of a t-structure and discuss some recent uses of t-structures on categories of coherent sheaves in (geometric) representation theory. After reviewing some traditional methods to obtain t-structures I will present a new construction that uses categorical Lie actions. As an application one recovers the category of "exotic sheaves", used in a recent proof of Lusztig's conjectures on a canonical bases for the Grothendieck group of Springer fibers by Bezrukavnikov and Mirković. The new construction is purely geometric, instead of using deep results from modular representation theory. This is joint work with Sabin Cautis.
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Eldad Haber
Departments of Mathematics, Earth and Ocean Science, UBC
Tue 25 Oct 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Mimetic Multiscale Methods and their application to Maxwell's equations
ESB 4133 (PIMS Lounge)
Tue 25 Oct 2016, 12:30pm-1:30pm

Abstract

Solving Maxwell's equations for earth science applications requires the discretization of large domains with sufficiently small mesh to capture local conductivity variation. Multiscale methods are discretization techniques that allow to use a coarse mesh and still obtain accuracy that is obtained through finer meshes. However, when considering the multiscale solution of vector equations, basic operator properties are not conserved. In this talk we will show how to extend multiscale methods for vector quantities and demonstrate their use for Maxwell's equations.
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McGill University
Tue 25 Oct 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB2012
Curvature flows and the isoperimetric problems in geometry
ESB2012
Tue 25 Oct 2016, 3:30pm-4:30pm

Abstract

 
Abstract: We will discuss two types of curvature flows designed to prove isoperimetric type inequalities. The first one is a mean curvature type flow, it was introduced in a previous joint work with Junfang Li in space forms. In a recent joint paper with Junfang Li and Mu-Tao Wang, we consider a similar normalized hypersurface flow in the more general ambient setting of warped product spaces with general base. Under a natural necessary condition, the flow preserves the volume of the bounded domain enclosed by a graphical hypersurface, and monotonically decreases the hypersurface area. Under another condition with is related to the notion of “photon sphere” in general relativity, we establish the regularity and convergence of the flow, thereby solve the isoperimetric problem in warped product spaces. In a similar spirit, I will discuss a inverse mean curvature type flow in hyperbolic space to deal with Alexandrov-Fenchel type isoperimetric inequalities. 
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Brian Chan
UBC
Tue 25 Oct 2016, 4:00pm
Discrete Math Seminar
ESB 4127
A Hard Problem in Lattice Theory
ESB 4127
Tue 25 Oct 2016, 4:00pm-5:00pm

Abstract

 Lattice theory is the study of an intriguing class of partially ordered sets known as lattices. Within this subject, there are many hard open problems. One such problem is to determine which countable lattices are sublattices of free lattices. In this talk, we will describe past progress on this problem and propose possible methods of attack using finite and finite width lattices. This research was done while I was a masters student at the University of Calgary.
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Université de Montréal
Wed 26 Oct 2016, 1:45pm
Mathematical Biology Seminar
PIMS (ESB 4th floor)
Feedback, delays and oscillations in blood cell production
UBC Math
Wed 26 Oct 2016, 3:00pm
Probability Seminar
ESB 2012
Models of Gradient Type with Sub-Quadratic Action
ESB 2012
Wed 26 Oct 2016, 3:00pm-4:00pm

Abstract

We consider models of gradient type, which is the density of a collection of real-valued random variables \phi :=\{\phi_x: x \in \Lambda\} given by Z^{-1}\exp({-\sum\nolimits_{j \sim k}V(\phi_j-\phi_k)}). We focus our study on the case that V(\nabla\phi) = [1+(\nabla\phi)^2]^\alpha with 0 < \alpha < 1/2, which is a non-convex potential. We introduce an auxiliary field t_{jk} for each edge and represent the model as the marginal of a model with log-cancave density. Based on this method, we prove that finite moments of the fields \left<[v \cdot \phi]^p \right> are bounded uniformly in the volume. This leads to the existence of infinite volume measures. Also, every ergodic infinite volume Gibbs measure with mean zero for the potential V above scales to a Gaussian free field.

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NTNU Norwegian University of Science and Technology
Wed 26 Oct 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Freaks of algebra -- a topologist's exhibition
ESB 4133 (PIMS Lounge)
Wed 26 Oct 2016, 3:15pm-4:15pm

Abstract

For this survey talk I will bring a bestiary of algebraic structures that are often less well known than they deserve to be. As I will explain, these are all related to symmetries and topology, and they have interesting symmetries of their own. This observation leads to new homology computations, and those will be the results that I will present along the way. Part of this work is joint with N. Wahl.

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Université de Savoie, Chambéry
Thu 27 Oct 2016, 3:30pm
Number Theory Seminar
MATH 126
Wave front sets of distributions in non-archimedean analysis
MATH 126
Thu 27 Oct 2016, 3:30pm-5:15pm

Abstract

In 1969, Sato and Hörmander introduced the notion of wave front set of a distribution in the real context. This concept gives a better understanding of operations on distributions such as product or pullback and it plays an important role in the theory of partial differential equations. In 1981, Howe introduced a notion of wave front set for some Lie group representations and in 1985, Heifetz gave an analogous version in the p-adic context. In this talk, in the t-adic context in characteristic zero, using Cluckers-Loeser motivic integration we will present analogous constructions of test functions, distributions and wave front sets. In particular, we will explain how definability can be used as a substitute for topological compactness of the sphere in the real and p-adic contexts to obtain finiteness. This a joint work with R. Cluckers, and F. Loeser.
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McGill
Fri 28 Oct 2016, 11:10am SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)
Nonpositive Immersions and Counting Cycles
ESB 4133 (PIMS Lounge)
Fri 28 Oct 2016, 11:10am-12:10pm

Abstract

The "nonpositive immersion" property is a condition on a 2-complex X that generalizes being a surface. When X has this property, its fundamental group appears to have has some very nice properties which I will discuss. I will spend the remainder of the talk outlining a proof that the nonpositive immersion property holds for a 2-complex obtained by attaching a single 2-cell to a graph. This was proven recently with Joseph Helfer and also independently by Lars Louder and Henry Wilton.
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McGill University
Fri 28 Oct 2016, 3:00pm
Department Colloquium
ESB 2012
CRM-Fields-PIMS Award Lecture: The Cubical Route to Understanding Groups
ESB 2012
Fri 28 Oct 2016, 3:00pm-4:00pm

Abstract

Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that have recently culminated in the resolution of the virtual Haken conjecture for 3-manifolds, and simultaneously dramatically extended our understanding of many infinite groups.

Note for Attendees

Refreshments (A light reception) are served in ESB 4133 from 2:30pm-3:00pm before the colloquium.
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Yale University
Mon 31 Oct 2016, 3:00pm
Algebraic Geometry Seminar
MATX 1102
The torsion order of an algebraic variety
MATX 1102
Mon 31 Oct 2016, 3:00pm-4:00pm

Abstract

 The minimal multiple of the diagonal to admit a decomposition in the sense of Bloch and Srinivas is called the torsion order of a smooth projective variety. It is bounded above by the greatest common divisor of the degrees of all unirational parameterizations, and is a stable birational invariant. Recently, a degeneration method initiated by Voisin, and developed by Colliot-Thélène and Pirutka, has led to a breakthrough in establishing lower bounds for the torsion order, hence obstructions to stable rationality. The power of this method lies in its mix of inputs from algebraic cycles, Hodge theory, algebraic K-theory, birational geometry, and singularity theory. I will survey the state of the art of this theory, which includes recent work of Chatzistamatiou and Levine, as well as provide some new examples.
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UBC
Mon 31 Oct 2016, 3:00pm
Harmonic Analysis Seminar
MATH 126
Linear and trilinear Kakeya-type estimates in R^4
MATH 126
Mon 31 Oct 2016, 3:00pm-4:00pm

Abstract

A Besicovich set is a compact subset of R^d that contains a unit line segment pointing in every direction. The Kakeya conjecture asserts that every Besicovich set in R^d must have dimension d. I will discuss some new trilinear Kakeya-type bounds in R^4, and how these bounds can be used to obtain improved bounds on the dimension of certain sets in R^4 that resemble Kakeya sets. This is joint work with Larry Guth.
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Northwestern
Mon 31 Oct 2016, 4:15pm
Algebraic Geometry Seminar
MATX 1102
The derived Maurer-Cartan locus
MATX 1102
Mon 31 Oct 2016, 4:15pm-5:15pm

Abstract

We give a new definition of the derived Maurer-Cartan locus MC^*(L), as a functor from differential graded Lie algebras to cosimplicial schemes, whose definition is sufficiently straightforward that it generalizes well to other settings such as analytic geometry. If L is differential graded Lie algebra, let L_+ be the truncation of L in positive degrees i>0. We prove that the differential graded algebra of functions on the cosimplicial scheme MC^*(L) is quasi-isomorphic to the Chevalley-Eilenberg complex of L_+, which is the usual definition of the derived Maurer-Cartan locus in characteristic zero.

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