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 Events
Oxford University
Thu 18 Jan 2018, 11:00am SPECIAL
Mathematical Biology Seminar / Probability Seminar
Math 126
Modelling mutations: mechanisms and evolutionary consequences
Math 126
Thu 18 Jan 2018, 11:00am-12:00pm

Abstract

 As the source of new genetic variation, mutations constitute a fundamental process in evolution. While most mutations lower fitness, rare beneficial mutations are essential for adaptation to changing environments. Thus, understanding the effects of mutations and estimating their rate is of strong interest in evolutionary biology. The necessity to treat rare mutational events stochastically has also stimulated a rich mathematical literature. Typically, mutations are modelled simply as an instantaneous change of type, occurring at a fixed rate. However, the underlying biology is more complex. I will present two recent projects delving deeper into mutational mechanisms and their consequences. Firstly, mutations can exhibit a multi-generational delay in phenotypic expression. Secondly, individuals within a population can vary in their propensity to mutate. Through analytical and simulation methods, we investigated the impact of these biological complexities on (a) population fitness and capacity to evolve, and (b) our ability to accurately infer mutation rates from data. I will conclude by discussing some future directions to incorporate these insights into more realistic models and to quantify the distribution of mutation rate empirically.

Note for Attendees

 Math 126 is behind a locked glass door. Latecomers without access should knock loudly!
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Kornelia Hera
Eotvos Lorand University, Budapest
Fri 19 Jan 2018, 2:00pm
Harmonic Analysis Seminar
MATH 126
Furstenberg-type estimates for unions of affine subspaces
MATH 126
Fri 19 Jan 2018, 2:00pm-3:00pm

Abstract

A plane set is called a t-Furstenberg set for some t in (0,1), if it has an at least t-dimensional intersection with some line in each direction (here and in the sequel dimension refers to Hausdorff dimension).  Classical results are that every t-Furstenberg set has dimension at least 2t, and at least t + 1/2.

We generalize these estimates for families of affine subspaces. As a result, we prove that the union of any s-dimensional family of k-dimensional affine subspaces is at least k + s/(k+1) -dimensional, and is exactly k + s -dimensional if s is at most 1.

Based on joint work with Tamas Keleti and Andras Mathe.
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Oxford University
Fri 19 Jan 2018, 3:00pm SPECIAL
Department Colloquium
ESB 2012
Stochastic population dynamic models with applications to pathogen evolution
ESB 2012
Fri 19 Jan 2018, 3:00pm-4:00pm

Abstract

Biological populations facing severe environmental change must adapt in order to avoid extinction. This so-called “evolutionary rescue” scenario is relevant to many applied problems, including pathogen evolution of drug resistance during the treatment of infectious diseases. Understanding what drives the rescue process gives rise to interesting mathematical modelling challenges arising from two key features: demographic and evolutionary processes occur on the same timescale, and stochasticity is inherent in the emergence of rare well-adapted mutants. In this talk, I will present recent work on population dynamics in changing environments, merging biological realism with tractable stochastic models. Firstly, I will describe a model of drug resistance evolution in chronic viral infections, which serves as a case study for a novel mathematical approach yielding analytical approximations for the probability of rescue. Secondly, I will present a combined theoretical and experimental investigation of the classical problem of establishment (non-extinction) of new lineages, using antibiotic-resistant bacteria as a model system. Finally, I will discuss some future directions in modelling antibiotic treatment to predict optimal dosing strategies, and in developing a general theoretical framework for evolutionary rescue that unites approaches to distinct applied problems.

Note for Attendees

Refreshments will be served at 2:45 p.m. in ESB 4133, the PIMS Lounge.
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Jay Newby
University of North Carolina, Chapel Hill
Mon 22 Jan 2018, 12:00pm SPECIAL
ESB 4133 (PIMS Lounge)
Seminar Talk in Math Biology, Applied Stochastics: How molecular crowding is changing our understanding of spatial patterning in living cells
ESB 4133 (PIMS Lounge)
Mon 22 Jan 2018, 12:00pm-1:00pm

Details


Molecular crowding has recognized consequences for biological function. However, there are also circumstances in which un-crowding is important that is, when molecules must evacuate from a region before a given process can occur. One example is offered by the T cell, where large surface molecules must evacuate from a region to allow for the T cell to interact with its target, thereby facilitating immune function. Evacuation is fundamentally stochastic and spatial, since diffusion is a major driver. Studies of molecular evacuation present mathematical and computational challenges. For example, in some scenarios, it is a "rare event", making straightforward simulation unfeasible. To obtain a complete picture of diffusional evacuation, we use a combination of perturbation theory and numerical simulation. I will also show evidence of persistent un-crowding in living fungal cells. Based on our understanding of diffusional evacuation, we know that diffusion alone cannot explain these observations. I will discuss our current efforts to quantify and resolve how fungal cells control un-crowding.

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Cornell Statistical Science and Biological Statistics & Computational Biology
Mon 22 Jan 2018, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
An ODE to Statistics: Inference about Nonlinear Dynamics
ESB 2012
Mon 22 Jan 2018, 3:00pm-4:00pm

Abstract

Ordinary differential equation models are used extensively within mathematics as descriptions of processes in the real world. However, they are rarely employed by statisticians and there is a paucity of methods for combining differential equation models with data. This talk provides a survey of recently developed statistical methods for estimating parameters from data, conducting model criticism and improvement for differential equation models in the light of data, and designing experiments that yield optimal estimates of parameters. It ends with some perspectives on the current state of the field and open problems.

Note for Attendees

Reception before the talk in ESB 4133 (the PIMS lounge). This is in the IAM/PIMS distinguished speaker series.
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Saskatchewan
Mon 22 Jan 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
Asymptotic geometry of hyperpolygons
MATH 126
Mon 22 Jan 2018, 4:00pm-5:00pm

Abstract

Nakajima quiver varieties lie at the interface of geometry and representation theory.  I will discuss a particular example, hyperpolygon space, which arises from star-shaped quivers.  The simplest of these varieties is a noncompact complex surface admitting the structure of an "instanton", and therefore fits nicely into the Kronheimer-Nakajima classification of ALE hyperkaehler 4-manifolds, which is a geometric realization of the McKay correspondence for finite subgroups of SU(2).  For more general hyperpolygon spaces, we speculate on how this classification might be extended by studying the asymptotic geometry of the variety.  In moduli-theoretic terms, this involves driving the stability parameter for the quotient to an irregular value.  This is joint work in progress with Harmut Weiss, building on previous work with Jonathan Fisher.
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Jay Newby
University of North Carolina, Chapel Hill
Tue 23 Jan 2018, 3:45pm SPECIAL
Department Colloquium
ESB 2012 (PIMS)
Weaker is better: how weak transient molecular interactions give rise to robust, dynamic immune protection
ESB 2012 (PIMS)
Tue 23 Jan 2018, 3:45pm-4:45pm

Abstract

The longstanding view in chemistry and biology is that high-affinity, tight-binding interactions are optimal for many essential functions, such as receptor-ligand interactions. Yet, an increasing number of biological systems are emerging that challenge this view, finding instead that low-affinity, rapidly unbinding dynamics can be essential for optimal function. These mechanisms have been poorly understood in the past due to the inability to directly observe such fleeting interactions and the lack of a theoretical framework to mechanistically understand how they work. In fact, it is only by tracking the motion of effector nanoprobes that afford detection of multiple such interactions simultaneously, coupled with inferences by stochastic modeling, Bayesian statistics, and bioimaging tools, that we recently begin to obtain definitive evidence substantiating the consequences of these interactions. A common theme has begun to emerge: rapidly diffusing third-party molecular anchors with weak, short-lived affinities play a major role for self organization of micron-scale living systems. My talk will demonstrate how these ideas can answer a longstanding question: how mucosal barriers selectively impede transport of pathogens and toxic particles, while allowing diffusion of nutrients.
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UBC
Wed 24 Jan 2018, 3:10pm
Probability Seminar
LSK 460
Heat flow on snowballs
LSK 460
Wed 24 Jan 2018, 3:10pm-4:10pm

Abstract

Quasisymmetric maps are fruitful generalizations of conformal maps. Quasisymmetric uniformization problem seeks for extensions of uniformization theorem beyond the classical context of Riemann surfaces.

The goal of this talk is to show that quasisymmetric uniformization problem is closely related to random walks and diffusions. I will explain how the existence of quasisymmetric maps is equivalent to heat kernel estimates for the simple random walk on a family of planar graphs. The same methods also apply to diffusions on a class of fractals homeomorphic to the 2-sphere.

These ideas will be illustrated using snowballs and their graph approximations. Snowballs are high dimensional analogues of Koch snowflake.

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Courant Institute, NYU
Wed 24 Jan 2018, 3:15pm
Mathematical Biology Seminar
PIMS Lounge, ESB 4133
Mechanical Positioning of Multiple Myonuclei in Muscle Cells
PIMS Lounge, ESB 4133
Wed 24 Jan 2018, 3:15pm-4:15pm

Abstract

 Many types of large cells have multiple nuclei. In long muscle cells, nuclei are distributed almost uniformly along their length, which is crucial for cell function. However, the underlying positioning mechanisms remain unclear. We examine computationally the hypothesis that a force balance generated by microtubules positions the nuclei. Rather than assuming what the forces are, we allow for various types of forces between pairs of nuclei and between the nuclei and the cell boundary. Mathematically, this means that we start with a great number of potential models. We then use a reverse engineering approach by screening the models and requiring their predictions to fit imaging data on nuclei positions from hundreds of muscle cells of Drosophila larva. Computational screens result in a small number of feasible models, the most adequate of which suggests that the nuclei repel each other and the cell boundary with forces that decrease with distance.

This suggests that microtubules growing from nuclear envelopes push on neighboring nuclei and the cell boundary. We support this hypothesis with stochastic microscopic simulations. Using statistical and analytical tools such as correlation and bifurcation analysis, we make several nontrivial predictions: An increased nuclear density near the cell poles, zigzag patterns in wider cells, and correlations between the cell width and elongated nuclear shapes, all of which we confirm by image analysis of the experimental data.

This is joint work with Mary Baylies, Alex Mogilner and Stefanie Windner.

 

 

Note for Attendees

Refreshments: PIMS tea will be served at 2:45 in ESB 4133.
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Alexander Bihlo
Mathematics and Statistics, Memorial University of Newfoundland
Thu 25 Jan 2018, 11:00am
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge) (please note the unusual date)
A well-balanced meshless tsunami propagation and inundation model
ESB 4133 (PIMS Lounge) (please note the unusual date)
Thu 25 Jan 2018, 11:00am-12:00pm

Abstract

We derive a universal criterion for the preservation of the lake at rest solution in general mesh-based and meshless numerical schemes for the shallow-water equations with bottom topography. The main idea is a careful mimetic design for the spatial derivative operators in the momentum flux equation that is paired with a compatible averaging rule for the water column height arising in the bottom topography source term. The resulting numerical schemes for the shallow-water equations are called well-balanced.

Based on a well-balanced RBF-FD discretization of the shallow-water equations, we develop a meshless tsunami propagation and inundation model. The moving wet-dry interface between the incoming wave and the shoreline is handled using RBF generated extrapolation, yielding a truly meshless tsunami model. Several numerical results are presented that demonstrate excellent agreement of the resulting model with standard one- and two-dimensional benchmark tests.

This is joint work with Rüdiger Brecht, Scott MacLachlan and Jörn Behrens. 
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Harvard University
Thu 25 Jan 2018, 4:00pm SPECIAL
PIMS Seminars and PDF Colloquiums
ESB 2012, UBC
Values of the zeta function at negative integers, from Euler to the trace formula
ESB 2012, UBC
Thu 25 Jan 2018, 4:00pm-5:00pm

Abstract

Although the zeta function \zeta(s) is often named after Riemann, it was Euler who discovered many of its remarkable properties. After making his name on the evaluation of \zeta(2), Euler was able to obtain similar formulas at all positive even integers, and defined putative values at negative integers, where the series does not converge. Euler showed these values at negative integers were all rational numbers. A comparison with the values at positive integers led him to guess the functional equation relating \zeta(s) to \zeta(1-s) (which was proved about one hundred years later by Riemann). I will begin by exposing some of this work, then show how the values at negative integers can be used to compute the dimension of certain spaces of automorphic forms. In a special case the dimension turns out to be 1, and this leads to a construction of local systems with exceptional Galois groups on the projective line (minus two points) over a finite field.
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Courant Institute, NYU
Fri 26 Jan 2018, 3:00pm
Department Colloquium
ESB 2012
Traveling Waves in Cell Populations
ESB 2012
Fri 26 Jan 2018, 3:00pm-4:00pm

Abstract

PDE models can be a powerful tool for understanding emerging structures and patterns, such as aggregates and traveling waves formed by large populations of cells. As a specific example, I will discuss myxobacteria, which, due to their co-operative nature, lie on the boundary between uni- and multicellular organisms. I will present a novel age-structured, continuous macroscopic model. The derivation is based on simple interaction rules and set within the SOH (Self-Organized Hydrodynamics) framework. The strength of this combined approach is that microscopic information can be incorporated into the particle model in a straight-forward manner, whilst the continuous model can be analyzed using mathematical tools, such as stability and asymptotic analysis.

It has been suggested that myxobacteria are not able to react to signals immediately after they have reversed their direction. Our analysis reveals that this insensitivity period is not necessary for wave formation, but is essential for wave synchronization. A more mathematical focus will be the existence and stability of such traveling waves moving in two opposing waves frames. Fascinatingly, while the wave profiles do not change, the wave composition does, and the fractions of reversible and non- reversible bacteria form waves traveling in the opposite direction. I will discuss the explicit construction of such waves and show simulation results.

This is joint work with Pierre Degond and Hui Yu.

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Frederico Scavia
UBC
Mon 29 Jan 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
TBA
MATH 126
Mon 29 Jan 2018, 4:00pm-5:00pm

Abstract

 
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UBC
Wed 31 Jan 2018, 3:10pm
Probability Seminar
LSK 460
TBA
LSK 460
Wed 31 Jan 2018, 3:10pm-4:10pm

Abstract

 
TBA
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University of British Columbia
Wed 31 Jan 2018, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
TBA
ESB 4133 (PIMS Lounge)
Wed 31 Jan 2018, 3:15pm-4:15pm

Abstract

 
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UBC
Mon 5 Feb 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
TBA
MATH 126
Mon 5 Feb 2018, 4:00pm-5:00pm

Abstract

 TBA
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Indiana University
Tue 6 Feb 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
ESB 2012
Tue 6 Feb 2018, 3:30pm-4:30pm

Abstract

 
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School of Interactive Computing College of Computing GeorgiaTech
Mon 26 Feb 2018, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
TBA
ESB 2012
Mon 26 Feb 2018, 3:00pm-4:00pm

Abstract

 

Note for Attendees

Reception before the talk in ESB 4133 (the PIMS lounge). This talk is in the IAM/PIMS distinguished speaker series. 
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SNS, Pisa
Fri 2 Mar 2018, 3:00pm SPECIAL
Department Colloquium
ESB2012
PIMS-UBC Distinguished Colloquium--Some specialization problems in Geometry and Number Theory
ESB2012
Fri 2 Mar 2018, 3:00pm-4:00pm

Abstract

We shall survey over the general issue of
`specializations which preserve a property',
for a parametrized family of algebraic varieties.
We shall limit ourselves to a few examples.
We shall start by recalling typical contexts like
Bertini and Hilbert Irreducibility theorems,
illustrating some new result.
Then we shall jump to much more recent instances,
related to algebraic families of abelian varieties.

Note for Attendees

Refreshments will be served in ESB 4133 from 2:45 p.m.-3:00 p.m.
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University of Washington
Mon 5 Mar 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
TBA
MATH 126
Mon 5 Mar 2018, 4:00pm-5:00pm

Abstract

 TBA
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McGill
Tue 6 Mar 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
TBA
ESB 2012
Tue 6 Mar 2018, 3:30pm-4:30pm

Abstract

 
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Harvard University.
Tue 6 Mar 2018, 4:00pm
Discrete Math Seminar
ESB 4127
TBD
ESB 4127
Tue 6 Mar 2018, 4:00pm-5:00pm

Abstract

 
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Université Laval
Thu 8 Mar 2018, 3:30pm SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Introduction to Supersingular Iwasawa Theory of Elliptic Curves
ESB 4127
Thu 8 Mar 2018, 3:30pm-5:15pm

Abstract

Let E/Q be an elliptic curve. In Iwasawa Theory, we study the behaviours of E over a tower of number fields. For example, it is known that the Mordell Weil ranks of E over all p-power cyclotomic extensions of Q are bounded when p does not divide the conductor of E. Surprisingly, the techniques required to show this are very different depending on the number of points on the finite curve when we consider E reduced modulo p. The easier case is when E has "ordinary" reduction at p and the more difficult case is when E has "supersingular" reduction at p. I will review the Iwasawa-theoretic tools used to study the behaviours of E over cyclotomic fields in these two cases. I will also discuss some recent developments on the Iwasawa theory of elliptic curves over quadratic extensions of Q.

This talk is part of the PIMS Thematic Events on "Galois groups in arithmetic".
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TBA
UBC Math
Fri 9 Mar 2018, 3:00pm
Department Colloquium
ESB 2012
Graduate Research Award: TBA
ESB 2012
Fri 9 Mar 2018, 3:00pm-4:00pm

Abstract


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Edmonton
Mon 12 Mar 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
TBA
MATH 126
Mon 12 Mar 2018, 4:00pm-5:00pm

Abstract

 TBA
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University of Washington
Wed 14 Mar 2018, 3:10pm
Probability Seminar
LSK 460
TBA
LSK 460
Wed 14 Mar 2018, 3:10pm-4:10pm

Abstract

 
TBA
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Concordia University
Thu 15 Mar 2018, 3:30pm SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
p-Adic modular forms
ESB 4127
Thu 15 Mar 2018, 3:30pm-5:15pm

Abstract

Abstract: p-Adic modular forms have first been defined by J.-P. Serre as q-expansions and have later been interpreted geometrically by N. Katz as sections of certain modular line bundles over the ordinary locus of the relevant modular curves.
Katz also defined overconvergent modular forms of integer weights as overconvergent sections of the modular line bundles of that weight. Many years later H. Hida and respectively R. Coleman defined ordinary, respectively finite slope overconvergent modular forms of arbitrary, p-adic weight as q-expansions and using these Coleman and Mazur constructed at the end of the 90's the famous eigencurve. Recently, together with Andreatta, Pilloni and Stevens we have been able to geometrically redefine the overconvergent modular forms of Hida and Coleman and so we were able to generalize these constructions to Hilbert and Siegel modular forms.

This talk is part of the PIMS Thematic Events on "Galois groups in arithmetic".
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TBA
UBC Math
Fri 16 Mar 2018, 3:00pm
Department Colloquium
ESB 2012
Graduate Research Award: TBA
ESB 2012
Fri 16 Mar 2018, 3:00pm-4:00pm

Abstract


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School of Sustainability, Arizona State
Mon 19 Mar 2018, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
TBA
ESB 2012
Mon 19 Mar 2018, 3:00pm-4:00pm

Abstract

 

Note for Attendees

Reception beforehand in ESB 4133 (the PIMS lounge). Marty is the distinguished IAM Alumni Lecturer this year. 
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Oregon
Mon 19 Mar 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
TBA
MATH 126
Mon 19 Mar 2018, 4:00pm-5:00pm

Abstract

 TBA
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University of California, Davis
Tue 20 Mar 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
TBA
ESB 2012
Tue 20 Mar 2018, 3:30pm-4:30pm

Abstract

 
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University of Washington
Wed 21 Mar 2018, 3:10pm
Probability Seminar
LSK 460
TBA
LSK 460
Wed 21 Mar 2018, 3:10pm-4:10pm

Abstract

 
TBA
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TBA
UBC Math
Fri 23 Mar 2018, 3:00pm
Department Colloquium
ESB 2012
Graduate Research Award: TBA
ESB 2012
Fri 23 Mar 2018, 3:00pm-4:00pm

Abstract


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Arizona State University
Tue 27 Mar 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
ESB 2012
Tue 27 Mar 2018, 3:30pm-4:30pm

Abstract

 
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MIT
Tue 27 Mar 2018, 4:00pm
Discrete Math Seminar
ESB 4127
TBD
ESB 4127
Tue 27 Mar 2018, 4:00pm-5:00pm

Abstract

 
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Jean-Marc Deshouillers
University of Bordeaux
Thu 29 Mar 2018, 3:30pm
Number Theory Seminar
TBA
Thu 29 Mar 2018, 3:30pm-5:00pm

Abstract


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Eberhard Karls University, Tuebingen
Tue 3 Apr 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
TBA
ESB 2012
Tue 3 Apr 2018, 3:30pm-4:30pm

Abstract

 
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Oxford
Thu 5 Apr 2018, 4:00pm SPECIAL
Algebraic Geometry Seminar
TBA
Thu 5 Apr 2018, 4:00pm-5:00pm

Abstract

 TBA
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University of Oxford
Fri 6 Apr 2018, 3:00pm
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium--TBA
ESB 2012
Fri 6 Apr 2018, 3:00pm-4:00pm

Abstract

 

Note for Attendees

Light refreshments will be served at 2:45pm in ESB 4133, the PIMS Lounge before this colloquium.
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Rafe Mazzeo
Stanford University
Tue 10 Apr 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
TBA
ESB 2012
Tue 10 Apr 2018, 3:30pm-4:30pm

Abstract

 
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UCLA
Fri 14 Sep 2018, 3:00pm
Department Colloquium
ESB 2012
TBA
ESB 2012
Fri 14 Sep 2018, 3:00pm-4:00pm

Abstract

 
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