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 Events
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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PennState
Mon 27 Oct 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Rozansky--Witten-type invariants from symplectic Lie pairs
ESB 4127 (host: UBC)
Mon 27 Oct 2014, 3:00pm-4:00pm

Abstract

 In 1997, Rozansky and Witten built new finite-type invariants of 3-manifolds from hyperkahler manifolds. It was later shown by Kontsevich and Kapranov that those invariants only depend on the holomorphic symplectic structure of the hyperkahler manifolds. Indeed Kapranov proved that these invariants may be considered as an analogue of Chern-Simons type invariants, where the Atiyah class of the underlying complex manifold plays the role of  Lie bracket. In this talk, we introduce symplectic structures on "Lie pairs" of (real or complex) algebroids, encompassing homogeneous symplectic spaces, symplectic manifolds with a $\mathfrak g$-action and holomorphic symplectic manifolds. We show that to each such symplectic Lie pair are associated Rozansky-Witten-type invariants of three-manifolds. This is a joint work with Yannick Voglaire.
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Wes Maciejewski
UBC, Dept of Mathematics & CWSEI
Tue 28 Oct 2014, 12:30pm
Lunch Series on Teaching & Learning
MATH 126
Do we know how students view mathematics and how they study it?
MATH 126
Tue 28 Oct 2014, 12:30pm-1:30pm

Abstract

It has long been known that the way a student views the subject they study affects the approach they take to studying
the subject. This, in turn, affects their performance in the subject. It seems, then, that the improvement of student
outcomes not only requires addressing the approach a student takes to study, but also their view of the subject. In this presentation, I will present results from a series of surveys intended to explore two separate, but related questions:
1. Do math instructors actually know how their students view math?
2. What approaches to study do students take and how do these relate to their achievement?
The crucial aspect of this work is that the data gathered was analysed by course year. It turns out that the answers to both questions above are different for lower and upper-year courses.
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Mingfeng Zhao
Tue 28 Oct 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Traveling waves involving fractional Laplacians
ESB 2012
Tue 28 Oct 2014, 3:30pm-4:30pm

Abstract

In this talk, we will discuss the existence of the traveling wave solution for the Allen-Cahn equation involving the fractional Laplacians. Based on the existence of the standing waves for the balanced Allen-Cahn equation, we will use the continuity method to obtain the existence of the traveling waves for unbalanced Allen-Cahn equation. The key ingredient is the the bound of the traveling speed in terms of the potential. Some open questions will be discussed.
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University of Utah
Wed 29 Oct 2014, 3:15pm
Topology and related seminars
ESB 4133
Constructing aspherical manifolds with a given fundamental group
ESB 4133
Wed 29 Oct 2014, 3:15pm-4:15pm

Abstract

While an aspherical complex is determined up to homotopy by its fundamental group, there are many geometrically different aspherical manifolds with the same fundamental group. For instance, the punctured torus and the pair of pants look quite different, but both have the same fundamental group F_2. I will discuss constructions of aspherical manifolds for a given fundamental group, talk about the smallest dimension of such a manifold for a given group and describe some geometric invariants that distinguish different aspherical manifolds with the same fundamental group. I will discuss this for right angled Artin groups (joint work with Mike Davis, Boris Okun and Kevin Schreve) and possibly also for duality groups.
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Emory University
Thu 30 Oct 2014, 3:30pm
Number Theory Seminar
room MATH 126
Hasse principles over function fields of p-adic curves
room MATH 126
Thu 30 Oct 2014, 3:30pm-4:30pm

Abstract

 
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Univeristy of Michigan
Fri 31 Oct 2014, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
Imaging with waves in complex environments (PIMS-IAM-UBC distinguished colloquium)
ESB 2012 (PIMS)
Fri 31 Oct 2014, 3:00pm-4:00pm

Abstract

The talk is concerned with the application of sensor array imaging in complex environments. The goal of imaging is to estimate the support of remote sources or strong reflectors using time resolved measurements of waves at a collection of sensors (the array). This is a challenging problem when the imaging environment is complex, due to numerous small scale inhomogeneities and/or rough boundaries that scatter the waves. Mathematically we model such complexity (which is necessarily uncertain in applications) using random processes, and thus study imaging in random media. I will focus attention on the application of imaging in random waveguides, which exhibits all the challenges of imaging in random media. I will present a quantitative study of cumulative scattering effects in such waveguides and then explain how we can use such a study to design high fidelity imaging methods.

Note for Attendees

Coffee, tea and cookies served at 2:30pm in the PIMS Lounge, ESB 4133.
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UBC
Mon 3 Nov 2014, 3:00pm
Harmonic Analysis Seminar
Math 204
Restriction theory and quadratic equations in dense variables
Math 204
Mon 3 Nov 2014, 3:00pm-4:00pm

Abstract


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Mathematics, Guelph
Mon 3 Nov 2014, 3:00pm SPECIAL
Institute of Applied Mathematics
LSK 460
The Good, the Bad, and the Ugly: From Biofilms to Mathematics and Back Again
LSK 460
Mon 3 Nov 2014, 3:00pm-4:00pm

Abstract

Bacterial biofilms are microbial depositions that form on immersed surfaces wherever environmental conditions sustain bacterial growth. They have been called the most successful life form on Earth and cities of microbes. Biofilms have important applications in environmental engineering, but are detrimental in a medical or industrial context. They have been characterised as both, spatially structured microbial populations, and as mechanical objects. Life in biofilm communities significantly differs from life in planktonic cultures. This is reflected in the complexity of mathematical models of biofilms that are essentially more involved than models of suspended microbial communities. In this talk I will focus on a class of highly degenerate diffusion-reaction biofilm models. In its simplest form this includes simultaneously two nonlinear diffusion effects: (i) a porous medium equation like degeneracy when the dependent variable biomass density vanishes, and (ii) a super-diffusion singularity when it attains its {\it a priori} known upper bound. I will summarize some analytical (well-posedness) results, and discuss applications of the model to answer questions about biofilms by numerical simulations. I will hereby focus on the contribution of mathematical models (this and others) to understand the formation of cluster-and-channel biofilm architectures, and I will illustrate how our model framework, extended by a model of bacterial communication by quorum sensing, can be used to shed light on the transition from an initial mode of biofilm colonization to a protected mode of biofilm growth.
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Kyoto University
Tue 4 Nov 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
TBA
ESB 2012
Tue 4 Nov 2014, 3:30pm-4:30pm

Abstract

 
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Justin Chan
SFU
Tue 4 Nov 2014, 4:00pm
Discrete Math Seminar
ESB 4127
An infinite family of inv-Wilf-equivalent permutation pairs
ESB 4127
Tue 4 Nov 2014, 4:00pm-5:00pm

Abstract

Wilf-equivalence is one of the central concepts of pattern-avoiding permutations, and has been studied for more than thirty years. The two known infi nite families of Wilf-equivalent permutation pairs, due to Stankova-West and Backelin-West-Xin, both satisfy the stronger condition of shape-Wilf-equivalence. Dokos et al. recently studied a di fferent strengthening of Wilf-equivalence called inv-Wilf-equivalence, which takes account of the inversion number of a permutation. They conjectured that all inv-Wilf-equivalent permutation pairs arise from trivial symmetries. We disprove this conjecture by constructing an infi nite family of counterexamples derived from the permutation pair (231) and (312). The key to this construction is to generalize simultaneously the concepts of shape-Wilf-equivalence and inv-Wilf-equivalence. A further consequence is a proof of the recent Baxter-Jaggard conjecture on even-shape-Wilf-equivalent permutation pairs.
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Bonn
Wed 5 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
TBA
ESB 4127 (host: UAlberta)
Wed 5 Nov 2014, 3:00pm-4:00pm

Abstract

 TBA
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Yariv Mizrahi
Thu 6 Nov 2014, 12:30pm
One Time Event
Room 200 of the Graduate Student Centre
Doctoral Exams
Room 200 of the Graduate Student Centre
Thu 6 Nov 2014, 12:30pm-10:00am
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UBC
Thu 6 Nov 2014, 12:30pm
Graduate Student Seminar
Math 225
Supersymmetric integration
Math 225
Thu 6 Nov 2014, 12:30pm-1:45pm

Abstract

We begin by defining the Grassmann integral of a function of both commuting ("bosonic") and anti-commuting ("fermionic") variables. An important example is the mixed bosonic-fermionic ("supersymmetric") Gaussian integral, which exhibits a surprising self-normalization property. Time permitting, we will mention applications of the Grassmann integral to the representation of self-avoiding walk as a supersymmetric quantum field theory.
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Uriya First
UBC
Thu 6 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
TBA
room MATH 126
Thu 6 Nov 2014, 3:30pm-4:30pm

Abstract

 
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Berkeley
Fri 7 Nov 2014, 1:30pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
TBA
ESB 4127 (host: UBC)
Fri 7 Nov 2014, 1:30pm-2:30pm

Abstract

 TBA
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UBC
Mon 10 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
TBA
ESB 4127 (host: UBC)
Mon 10 Nov 2014, 3:00pm-4:00pm

Abstract

 TBA
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UAlberta
Wed 12 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
TBA
ESB 4127 (host: UAlberta)
Wed 12 Nov 2014, 3:00pm-4:00pm

Abstract

 TBA
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Morningside Center of Mathematics and Purdue
Thu 13 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
Introduction to Mochizuki's works on inter-universal Teichmuller theory
room MATH 126
Thu 13 Nov 2014, 3:30pm-4:30pm

Abstract

Inter-universal Teichmuller theory, as developed by Mochizuki in the past decade, is an analogue for number fields of the classical Teichmuller theory, and also of the p-adic Teichmuller theory of Mochizuki. In this theory, the ring structure of a number field is subject to non-ring theoretic deformation. Absolute anabelian geometry, a refinement of anabelian geometry, plays a crucial role in inter-universal Teichmuller theory. In this talk, we will try to give an introduction to these ideas.
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UC Berkeley
Fri 14 Nov 2014, 3:00pm
Department Colloquium
MATX 1100
The fundamental theorem of arithmetic for metric measure spaces
MATX 1100
Fri 14 Nov 2014, 3:00pm-4:00pm

Abstract

A metric measure space (mms) is simply a complete, separable metric space equipped with a probability measure that has full support.  A fundamental insight of Gromov is that the space of such objects is much ``tamer'' than the space of complete, separable metric spaces per se because mms carry within themselves a canonical family of approximations by finite structures: one takes the random mms that arises from picking some number of points independently at random and equipping it with the induced metric and uniform probability measure.  A natural (commutative and associative) binary operation on the space of mms is defined by forming the Cartesian product of the two underlying sets equipped with the sum of the two metrics and the product of the two probability measures.  There is a corresponding notion of a prime  mms and an analogue of the fundamental theorem of arithmetic in the sense that any mms has a factorization into countably many prime mms which is unique up to the order of the factors.  Moreover,  a rich Fourier theory enables one to analyze convolutions of probability measures on the space of mms and obtain counterparts of classical results in the theory of infinitely divisible and stable probability measures on Euclidean spaces due to L\'evy, It\^o, Hin\u{c}in, and LePage.  This is joint work with Ilya Molchanov (Bern).

Note for Attendees

Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.
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Jussieu
Mon 17 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
TBA
ESB 4127 (host: UBC)
Mon 17 Nov 2014, 3:00pm-4:00pm

Abstract

 TBA
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Weiwei Ao
UBC
Tue 18 Nov 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
TBA
ESB 2012
Tue 18 Nov 2014, 3:30pm-4:30pm

Abstract

 
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TBA
Thu 20 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
room MATH 126
Thu 20 Nov 2014, 3:30pm-4:30pm

Abstract

 
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The University of Auckland
Fri 21 Nov 2014, 3:00pm
Department Colloquium
Math Annex 1100
Reducing lectures, making students responsible, and offering semi-authentic mathematical experiences.
Math Annex 1100
Fri 21 Nov 2014, 3:00pm-4:00pm

Abstract

 In the Mathematics Department of The University of Auckland a major research project into undergraduate mathematics learning outcomes has required the development of three innovative ways to deliver undergraduate mathematics. One of these involves reducing lectures to less than one per week, handing responsibility for most of their mathematical learning to students using web or text resources. We then use the staff time saved to provide semi-authentic mathematical experiences in which students work in small groups for up to two hours at a time guided by a lecturer on open-ended mathematical situations. Such sessions require new teaching skills and new learning orientations. There is some evidence that we have made progress on the development of mathematical process skills.
Our research shows that, with our small trial groups, students perform at similar levels on the conventional assessments as do the students in the standard courses.

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UAlberta
Mon 24 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
TBA
ESB 4127 (host: UBC)
Mon 24 Nov 2014, 3:00pm-4:00pm

Abstract

 TBA
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UAlberta
Wed 26 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
TBA
ESB 4127 (host: UAlberta)
Wed 26 Nov 2014, 3:00pm-4:00pm

Abstract

 TBA
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Oxford University
Thu 27 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126
TBA
room MATH 126
Thu 27 Nov 2014, 3:30pm-4:30pm

Abstract

 
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Case Western
Wed 3 Dec 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
TBA
ESB 4127 (host: UAlberta)
Wed 3 Dec 2014, 3:00pm-4:00pm

Abstract

 TBA
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Sat 10 Jan 2015, 9:00am SPECIAL
One Time Event
To Be Announced
Analysis - Qualifying Exams
To Be Announced
Sat 10 Jan 2015, 9:00am-12:00pm
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Sat 10 Jan 2015, 1:00pm SPECIAL
One Time Event
To Be Announced
Differential Equations - Qualifying Exams
To Be Announced
Sat 10 Jan 2015, 1:00pm-4:00pm
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Sat 10 Jan 2015, 1:00pm SPECIAL
One Time Event
To Be Announced Later
Algebra Qualifying Exams
To Be Announced Later
Sat 10 Jan 2015, 1:00pm-4:00pm
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Nicolaos Kapouleas
Brown University
Tue 13 Jan 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
TBA
ESB 2012
Tue 13 Jan 2015, 3:30pm-4:30pm

Abstract

 
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Caltech
Fri 30 Jan 2015, 3:00pm
Department Colloquium
ESB 2012 (PIMS) TBA (time and date to be confirmed)
PIMS-UBC distinguished colloquium
ESB 2012 (PIMS) TBA (time and date to be confirmed)
Fri 30 Jan 2015, 3:00pm-4:00pm

Abstract


Note for Attendees

Coffee, tea and cookies served at 2:30pm in the PIMS Lounge, ESB 4133.
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Brown University
Fri 13 Mar 2015, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
PIMS-UBC Distinguished Colloquium, TitleTBA
ESB 2012 (PIMS)
Fri 13 Mar 2015, 3:00pm-4:00pm

Abstract


Note for Attendees

Coffee, tea and cookies served at 2:30pm in the PIMS Lounge, ESB 4133.
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