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, 11:00am12:00pm
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 multigenerational 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.
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Eotvos Lorand University, Budapest

Fri 19 Jan 2018, 2:00pm
Harmonic Analysis Seminar
MATH 126

Furstenbergtype estimates for unions of affine subspaces

MATH 126
Fri 19 Jan 2018, 2:00pm3:00pm
Abstract
A plane set is called a tFurstenberg set for some t in (0,1), if it has an at least tdimensional intersection with some line in each direction (here and in the sequel dimension refers to Hausdorff dimension). Classical results are that every tFurstenberg 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 sdimensional family of kdimensional 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, 3:00pm4:00pm
Abstract
Biological populations facing severe environmental change must adapt in order to avoid extinction. This socalled “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 welladapted 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 (nonextinction) of new lineages, using antibioticresistant 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.
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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, 12:00pm1:00pm
Details
Molecular crowding has recognized consequences for biological function. However, there are also circumstances in which uncrowding 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 uncrowding 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 uncrowding.
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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, 3:00pm4:00pm
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.
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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, 4:00pm5:00pm
Abstract
Nakajima quiver varieties lie at the interface of geometry and representation theory. I will discuss a particular example, hyperpolygon space, which arises from starshaped quivers. The simplest of these varieties is a noncompact complex surface admitting the structure of an "instanton", and therefore fits nicely into the KronheimerNakajima classification of ALE hyperkaehler 4manifolds, 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 modulitheoretic 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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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, 3:45pm4:45pm
Abstract
The longstanding view in chemistry and biology is that highaffinity, tightbinding interactions are optimal for many essential functions, such as receptorligand interactions. Yet, an increasing number of biological systems are emerging that challenge this view, finding instead that lowaffinity, 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 thirdparty molecular anchors with weak, shortlived affinities play a major role for self organization of micronscale 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, 3:10pm4:10pm
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 2sphere.
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, 3:15pm4:15pm
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.
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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 wellbalanced meshless tsunami propagation and inundation model

ESB 4133 (PIMS Lounge) (please note the unusual date)
Thu 25 Jan 2018, 11:00am12:00pm
Abstract
We derive a universal criterion for the preservation of the lake at rest solution in general meshbased and meshless numerical schemes for the shallowwater 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 shallowwater equations are called wellbalanced.
Based on a wellbalanced RBFFD discretization of the shallowwater equations, we develop a meshless tsunami propagation and inundation model. The moving wetdry 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 twodimensional 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, 4:00pm5:00pm
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(1s) (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, 3:00pm4:00pm
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 cooperative nature, lie on the boundary between uni and multicellular organisms. I will present a novel agestructured, continuous macroscopic model. The derivation is based on simple interaction rules and set within the SOH (SelfOrganized Hydrodynamics) framework. The strength of this combined approach is that microscopic information can be incorporated into the particle model in a straightforward 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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UBC

Mon 29 Jan 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126

TBA

MATH 126
Mon 29 Jan 2018, 4:00pm5:00pm
Abstract
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UBC

Wed 31 Jan 2018, 3:10pm
Probability Seminar
LSK 460

TBA

LSK 460
Wed 31 Jan 2018, 3:10pm4:10pm
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, 3:15pm4:15pm
Abstract
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UBC

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

TBA

MATH 126
Mon 5 Feb 2018, 4:00pm5:00pm
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, 3:30pm4:30pm
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, 3:00pm4:00pm
Abstract
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SNS, Pisa

Fri 2 Mar 2018, 3:00pm
SPECIAL
Department Colloquium
ESB2012

PIMSUBC Distinguished ColloquiumSome specialization problems in Geometry and Number Theory

ESB2012
Fri 2 Mar 2018, 3:00pm4:00pm
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.
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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, 4:00pm5:00pm
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, 3:30pm4:30pm
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, 4:00pm5:00pm
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, 3:30pm5:15pm
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 ppower 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 Iwasawatheoretic 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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UBC Math

Fri 9 Mar 2018, 3:00pm
Department Colloquium
ESB 2012

Graduate Research Award: TBA

ESB 2012
Fri 9 Mar 2018, 3:00pm4:00pm
Abstract
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Edmonton

Mon 12 Mar 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126

TBA

MATH 126
Mon 12 Mar 2018, 4:00pm5:00pm
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, 3:10pm4:10pm
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

pAdic modular forms

ESB 4127
Thu 15 Mar 2018, 3:30pm5:15pm
Abstract
Abstract: pAdic modular forms have first been defined by J.P. Serre as qexpansions 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, padic weight as qexpansions 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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UBC Math

Fri 16 Mar 2018, 3:00pm
Department Colloquium
ESB 2012

Graduate Research Award: TBA

ESB 2012
Fri 16 Mar 2018, 3:00pm4:00pm
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, 3:00pm4:00pm
Abstract
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Oregon

Mon 19 Mar 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126

TBA

MATH 126
Mon 19 Mar 2018, 4:00pm5:00pm
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, 3:30pm4:30pm
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, 3:10pm4:10pm
Abstract
TBA
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UBC Math

Fri 23 Mar 2018, 3:00pm
Department Colloquium
ESB 2012

Graduate Research Award: TBA

ESB 2012
Fri 23 Mar 2018, 3:00pm4:00pm
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, 3:30pm4:30pm
Abstract
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MIT

Tue 27 Mar 2018, 4:00pm
Discrete Math Seminar
ESB 4127

TBD

ESB 4127
Tue 27 Mar 2018, 4:00pm5:00pm
Abstract
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University of Bordeaux

Thu 29 Mar 2018, 3:30pm
Number Theory Seminar

TBA

Thu 29 Mar 2018, 3:30pm5:00pm
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, 3:30pm4:30pm
Abstract
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Oxford

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

TBA

Thu 5 Apr 2018, 4:00pm5:00pm
Abstract
TBA
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University of Oxford

Fri 6 Apr 2018, 3:00pm
Department Colloquium
ESB 2012

PIMSUBC Distinguished ColloquiumTBA

ESB 2012
Fri 6 Apr 2018, 3:00pm4:00pm
Abstract
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Stanford University

Tue 10 Apr 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

TBA

ESB 2012
Tue 10 Apr 2018, 3:30pm4:30pm
Abstract
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UCLA

Fri 14 Sep 2018, 3:00pm
Department Colloquium
ESB 2012

TBA

ESB 2012
Fri 14 Sep 2018, 3:00pm4:00pm
Abstract
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Note for Attendees
Math 126 is behind a locked glass door. Latecomers without access should knock loudly!