Mathematics Dept.
  Events
Stanford University
Tue 2 Jan 2018, 12:30pm SPECIAL
Department Colloquium
MATH 102 (special time, lunch will be served)
Stability in the homology of configuration spaces
MATH 102 (special time, lunch will be served)
Tue 2 Jan 2018, 12:30pm-1:30pm

Abstract

This talk will illustrate some patterns in the homology of the configuration space F_k(M), the space of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.


Note for Attendees

Note special time. Lunch will be served.
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Stanford University
Wed 3 Jan 2018, 12:00pm SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)
Stability in the homology of Torelli groups
ESB 4133 (PIMS Lounge)
Wed 3 Jan 2018, 12:00pm-1:00pm

Abstract

The Torelli subgroups of mapping class groups are fundamental objects in low-dimensional topology, through some basic questions about their structure remain open. In this talk I will describe these groups, and how to use tools from representation theory to establish patterns their homology. This project is joint with Jeremy Miller and Peter Patzt. These "representation stability" results are an application of advances in a general algebraic framework for studying sequences of group representations.
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University of Adelaide
Wed 3 Jan 2018, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Equivariant formality of homogeneous spaces
ESB 4133 (PIMS Lounge)
Wed 3 Jan 2018, 3:15pm-4:15pm

Abstract

Equivariant formality, a notion in equivariant topology introduced by Goresky-Kottwitz-Macpherson, is a desirable property of spaces with group actions. Examples of equivariantly formal spaces include compact symplectic manifolds equipped with Hamiltonian compact Lie group actions and projective varieties equipped with linear algebraic torus actions. Less is known about compact homogeneous spaces G/K equipped with the isotropy action of K, which is not necessarily of maximal rank. In this talk we will review previous attempts of characterizing equivariant formality of G/K, and present our recent results on this problem using an analogue of equivariant formality in K-theory. Part of the work presented in this talk is joint with Jeffrey Carlson.
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University of Toronto
Thu 4 Jan 2018, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (PIMS)
Free Discontinuities in Optimal Transport
ESB 2012 (PIMS)
Thu 4 Jan 2018, 3:30pm-5:00pm

Abstract

Optimal maps in R^n to disconnected targets necessarily contain discontinuities (i.e.~tears). But how smooth are these tears? When the target components are suitably separated by hyperplanes, non-smooth versions of the implicit function theorem can be developed which show the tears are hypersurfaces given as differences of convex functions --- DC for short. If in addition the targets are convex the tears are actually C^{1,\alpha}. Similarly, under suitable affine independence assumptions, singularities of multiplicity k lie on DC rectifiable submanifolds of dimension n+1-k. These are stable with respect to W_\infty perturbations of the target measure. Moreover, there is at most one singularity of multiplicity n. This represents joint work with Jun Kitagawa.
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University of Lethbridge
Thu 4 Jan 2018, 3:30pm
Number Theory Seminar
MATH 126 Seminar Room
The sixth moment of the Riemann zeta function and ternary additive divisor sums
MATH 126 Seminar Room
Thu 4 Jan 2018, 3:30pm-4:30pm

Abstract

Hardy and Littlewood initiated the study of the 2k-th moments of the Riemann zeta function on the critical line. In 1918 Hardy and Littlewood established an asymptotic formula for the second moment and in 1926 Ingham established an asymptotic formula for the fourth moment. In this talk we consider the sixth moment of the zeta function on the critical line. We show that a conjectural formula for a certain family of ternary additive divisor sums implies an asymptotic formula for the sixth moment. This builds on earlier work of Ivic and of Conrey-Gonek.
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Kent State University
Mon 8 Jan 2018, 1:30pm
Harmonic Analysis Seminar
GEOG 201
Discrete maximal functions and the circle method
GEOG 201
Mon 8 Jan 2018, 1:30pm-2:30pm

Abstract

We will discuss some results concerning l^p boundedness of maximal functions related to diophantine problems which are susceptible to the circle method.
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Stanford University
Mon 8 Jan 2018, 3:00pm
Department Colloquium
ESB 2012 (note special time)
Dynamics, geometry, and the moduli space of Riemann surfaces
ESB 2012 (note special time)
Mon 8 Jan 2018, 3:00pm-4:00pm

Abstract

The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel.
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Joontae Kim
Mon 8 Jan 2018, 4:00pm SPECIAL
Algebraic Geometry Seminar
PIMS 4127
Wrapped Floer homology of real Lagrangians and volume growth of symplectomorphisms
PIMS 4127
Mon 8 Jan 2018, 4:00pm-5:00pm

Abstract

Floer homology has been a central tool to study global aspects of symplectic topology, which is based on pseudoholomorphic curve techniques proposed by Gromov. In this talk, we introduce a so-called wrapped Floer homology. Roughly speaking, this is a certain homology generated by intersection points of two Lagrangians and its differential is given by counting solutions to perturbed Cauchy-Riemann equation. We investigate an entropy-type invariant, called the slow volume growth, of certain symplectomorphisms and give a uniform lower bound of the growth using wrapped Floer homology. We apply our results to examples from real symplectic manifolds, including A_k-singularities and complements of a complex hypersurface. This is joint work with Myeonggi Kwon and Junyoung Lee.
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Stanford University
Tue 9 Jan 2018, 3:00pm SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)
Totally geodesic submanifolds of Teichmuller space and the Kontsevich-Zorich cocycle
ESB 4133 (PIMS Lounge)
Tue 9 Jan 2018, 3:00pm-4:00pm

Abstract

One of the ways we understand Teichmuller space, endowed with the Teichmuller metric, is by studying Teichmuller discs. They exist in great abundance: There is a Teichmuller disc through any point and in any direction. Typically, their projection to moduli space is dense, and yet infinitely often their projection is a closed subvariety of moduli space called a Teichmuller curve. Recently, in joint work with Eskin, McMullen, and Mukamel, we discovered the first non-trivial examples of higher dimensional analogues of Teichmuller discs, namely totally geodesic submanifolds.

In this talk, we will explain that such higher dimensional totally geodesic submanifolds are much more rigid and rare than Teichmuller discs: Each must cover a closed subvariety of moduli space, and only finitely many such subvarieties exist in each moduli space. This result is an application of joint work with Eskin and Filip on the Kontsevich-Zorich cocycle. One of the goals of the talk will be to explain what this cocycle is and why it lies at the heart of Teichmuller dynamics.
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UC-Davis
Tue 9 Jan 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Variational Problems on Arbitrary Sets
ESB 2012
Tue 9 Jan 2018, 3:30pm-4:30pm

Abstract

Let E be an arbitrary subset of R^n. Given real valued functions f defined on E and g defined on R^n, the classical obstacle problem asks for a minimizer of the Dirichlet energy subject to the following two constraints: (1) F = f on E and (2) F lies above g on R^n. In this talk, we will discuss how to use extension theory to construct (almost) solutions directly. We will also explain several recent results that will help lay the foundation for building a complete theory revolving around the belief that any variational problems that can be solved using PDE theory can also be dealt with using extension theory.
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Wed 10 Jan 2018, 2:45pm SPECIAL
PIMS Lounge
PIMS Afternoon Tea
PIMS Lounge
Wed 10 Jan 2018, 2:45pm-3:15pm

Details

The tea will be held on Wednesdays throughout the term starting on Wed. January 10th, 2018.
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University of Auckland
Wed 10 Jan 2018, 3:00pm
Probability Seminar
ESB 5104
Two locality properties in two dimensions
ESB 5104
Wed 10 Jan 2018, 3:00pm-4:00pm

Abstract


In two dimensions, many self-interacting processes are described by the Schramm-Loewner Evolution SLE(kappa), a family of random fractal path joining two boundary points of an underlying domain D.  These continuous paths arise as the scaling limits of various discrete self-interacting paths, such as loop-erased random walk.

A self-interacting process has the locality property if it does not "feel" the boundary of its domain D until it hits the boundary. Among the two-dimensional processes known as Schramm Loewner Evolution SLE(kappa), it is known that only one, SLE(6), satisfies the locality property.  In this talk, I will describe the key properties that identify SLE(6) - the Domain Markov Property, conformal invariance, and the (classical) Locality Property - and introduce a "non-local" form of locality also satisfied by SLE(6), describing the behaviour of the process when it first encloses a target set.

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ENS Lyon, France
Wed 10 Jan 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127
Mathematical model for sequential patterning of tooth signaling centers
ESB 4127
Wed 10 Jan 2018, 3:15pm-4:15pm

Abstract

Ectodermal derivatives such as teeth, hair, feathers or scales share similar morphological features and spatial patterning mechanisms. From the mathematical point of view, pioneering works of Alan Turing showed that spatial-temporal self-organization structures can emerge from reaction-diffusion systems. However, recent biological and mathematical studies give evidence that there is a substantial difference in pattern generation between static and growing domains. The latter may contain a key to understanding the problem of sequential patterning in developmental biology.

In this talk we present a macroscopic model of gene expression dynamics in the growing field where molars appear sequentially. Our model mimics the expression of the Edar gene during the formation of signaling centers, from where future teeth originate. We rely on a reaction-diffusion system of an activator-inhibitor type on a dynamically evolving tissue. The key element is not only the tissue growth but also its non-constant properties, which affect the reaction kinetics, depending on the presence of the activator. The purpose of the model is twofold. On one hand it describes a sequential formation of individual spots through Turing instability mechanism. On the other hand, it produces the activator up-regulation waves starting at distal field thanks to reaction functions containing bistable solutions. We present numerical studies of two dynamics on growing domain: under wild conditions and under a mutation regulating the inhibitor concentrations. For a fixed and fully matured domain, we analyze the effect of chemotaxis on the wavelength of Turing patterns and, as a consequence, on the merging of signaling centers that is observed in some biological conditions.
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UC San Diego
Thu 11 Jan 2018, 11:00am
Mathematics of Information and Applications Seminar
ORCH 3002
Phase retrieval from local measurements
ORCH 3002
Thu 11 Jan 2018, 11:00am-12:00pm

Abstract

We consider an instance of the phase-retrieval problem, where one wishes to recover a signal (viewed as a vector) from the noisy magnitudes of its inner products with locally supported vectors. Such measurements arise, for example, in ptychography, which is an imaging technique used in lense-less X-ray microscopes and in optical microscopes with increased fields of view.

Starting with the setup where the signal is one-dimensional, we present theoretical and numerical results on an approach that has two important properties. First, it allows deterministic (rather than random) measurement constructions, which we give examples of. Second, it uses a robust, fast recovery algorithm that consists of solving a system of linear equations in a lifted space, followed by simply calculating an eigenvector. We also present extensions, including to the two-dimensional setting.
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Kyle MacDonald
Fri 12 Jan 2018, 12:00pm
Graduate Student Seminar
MATH 225
What we talk about when we talk about spin
MATH 225
Fri 12 Jan 2018, 12:00pm-1:00pm

Abstract

You may have heard that if you rotate an electron through a full turn, then it points in the opposite direction from how it started. You may have tried to make sense of that by twisting your arms around in knots or turning in a circle until you fell over. And you may have overheard probabilists in this department talking about partition functions and magnetism, and wondered how it was all related.

Allow me to connect the dots with what I've learned while getting up to speed on the physics of spin systems. In the first part, we'll take a physics-style look at how the topology of rotation groups makes magnets work. In the second part, we'll use a classical identity in algebraic graph theory (Kirchoff's matrix-tree theorem) to work out some thermodynamic properties of ridiculously simplified materials. The only background required is undergraduate linear algebra. If you've diagonalized something in the last fifteen years, you're good.
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UC San Diego
Fri 12 Jan 2018, 3:00pm
Department Colloquium
ESB 2012
New and Improved Binary Embeddings of Data (and Quantization for Compressed Sensing with Structured Random Matrices)
ESB 2012
Fri 12 Jan 2018, 3:00pm-4:00pm

Abstract

We discuss two related problems that arise in the acquisition and processing of high-dimensional data. First, we consider distance-preserving fast binary embeddings. Here we propose fast methods to replace points from a set \mathcal{X} \subset \R^N with points in a lower-dimensional cube \{\pm 1\}^m, which we endow with an appropriate function to approximate Euclidean distances in the original space.
 
Second, we consider a problem in the quantization (i.e., digitization) of compressed sensing measurements. Here, we deal with measurements arising from the so-called bounded orthonormal systems and partial circulant ensembles, which arise naturally in compressed sensing applications. In both these problems we show state-of-the art error bounds, and to our knowledge, some of our results are the first of their kind.
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MIT
Mon 15 Jan 2018, 2:00pm SPECIAL
Topology and related seminars
ESB 4127
Floer transport and Lagrangian non-Abelianization
ESB 4127
Mon 15 Jan 2018, 2:00pm-3:00pm

Abstract

In this talk I will explain how to endow the moduli space of objects in certain wrapped Fukaya categories with a cluster structure. This will be achieved by counts of holomorphic disks between Lagrangians which are described by trivalent graphs. In particular, we will be recovering the Fock-Goncharov coordinates on the moduli space of flat connections on a surface and provide a symplectic interpretation for the non-Abelianization procedure via spectral networks.
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Cornell Physics and Mechanical & Aerospace Engineering
Mon 15 Jan 2018, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
From Newton's Law to Neurons
ESB 2012
Mon 15 Jan 2018, 3:00pm-4:00pm

Abstract

 Intended Audience: Public

 
Insects are first evolved to fly, and to fly is not to fall. How does an insect fly, why does it fly so well, and how can we infer its ‘thoughts’ from its flight dynamics? We have been seeking mechanistic explanations of the complex movement of insect flight. Starting from the Navier-Stokes equations governing the unsteady aerodynamics of flapping flight, we worked to build a theoretical framework for computing flight. This has led to new interpretations and predictions of the functions of an insect’s internal machinery that orchestrate its flight. I will discuss our recent computational and experimental studies of the balancing act of dragonflies and fruit flies: how a dragonfly recovers from falling upside-down and how a fly balances in air. In each case, the physics of flight informs us about the neural feedback circuitries underlying their fast reflexes.

Note for Attendees

There will be a reception before the talk in ESB 4133 (the PIMS lounge). This is a talk in the IAM/PIMS distinguished series.  
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MIT
Mon 15 Jan 2018, 4:00pm SPECIAL
Department Colloquium
MATH 100 (note special time and place)
The symplectic topology of affine varieties
MATH 100 (note special time and place)
Mon 15 Jan 2018, 4:00pm-5:00pm

Abstract

In this talk we will study complex affine varieties via symplectic topology. First, I will explain how to describe their complex structures, up to deformation, using Legendrian knots. Second, we will focus on the study of these Legendrian knots and provide techniques to distinguish them or show they are isotopic. Then, we will apply them to obtain new results about complex affine manifolds. In particular, we will recover the mirror symmetry functor from the perspective of Legendrian knot theory.

Note for Attendees

Refreshments will be served before this colloquium in MATH 125, the Math Lounge area, at 3:45 p.m.
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Oregon
Mon 15 Jan 2018, 5:00pm SPECIAL
Algebraic Geometry Seminar
Math 126 (note special time)
CANCELED - Exoflops
Math 126 (note special time)
Mon 15 Jan 2018, 5:00pm-6:00pm

Abstract

Consider a contraction pi: X -> Y from a smooth Calabi-Yau 3-fold to a singular one. (This is half of an "extremal transition;" the other half would be a smoothing of Y.) In many examples there is an intermediate object called an "exoflop" -- a category of matrix factorizations, derived-equivalent to X, where the critical locus of the superpotential looks like Y with a P^1 sticking out of it, and objects of D(X) that will be killed by pi_* correspond to objects supported at the far end of the P^1. I will discuss one or two interesting examples. This is joint work with Paul Aspinwall.
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Timm Treskatis
Mathematics, UBC
Tue 16 Jan 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
From Convex Optimisation to High-Resolution Finite Elements: Simulating Reactive Viscoplastic Fluid Flows
ESB 4133 (PIMS Lounge)
Tue 16 Jan 2018, 12:30pm-1:30pm

Abstract

What if we could imitate spider silk glands to produce biodegradable materials with properties similar to rubber or plastic? In our interdisciplinary team of fluid dynamicists, chemical engineers and material scientists, my role as mathematician is to try and answer this question from the numerical perspective. In this context, I am working on a problem of multiphase flow that includes advection, diffusion, chemical reaction, osmosis and viscoplastic behavior.

When it comes to the numerical solution of such a model that is based on a real-life problem, I am a strong advocate of so-called mimetic methods, i.e. discretisation schemes which preserve the physical properties of the system also at the discrete level. Following this philosophy,
* the transition between viscous flow and plastic creep is treated in a genuinely nonsmooth fashion and not simply smoothed out,
* the discretisation of the Navier-Stokes equations is pressure-robust,
* conservation of mass and momentum are respected,
* maximum principles are preserved,
* numerical diffusion is limited to an absolute minimum.

Additionally, the algorithm should clearly be stable, efficient and accurate for both steady and unsteady flow problems.

In this talk, I will show how we can couple fast algorithms from convex optimisation, a finite-element discretisation and algebraic flux correction to attain these objectives. Some videos of various flow configurations are included as well! 
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Nicolau Sarquis Aiex
UBC & PIMS
Tue 16 Jan 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
The space of min-max hypersurfaces
ESB 2012
Tue 16 Jan 2018, 3:30pm-4:30pm

Abstract

We use Lusternik-Schnirelmann Theory to study the topology of the space of closed embedded minimal hypersurfaces on a manifold of dimension between 3 and 7 and positive Ricci curvature. Combined with the works of Marques-Neves we can also obtain some information on the geometry of the minimal hypersurfaces they found.
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University of Auckland
Wed 17 Jan 2018, 3:10pm
Probability Seminar
LSK 460
The gaps left by a Brownian motion
LSK 460
Wed 17 Jan 2018, 3:10pm-4:10pm

Abstract


Run a Brownian motion on a torus for a long time.  How large are the

random gaps left behind when the path is removed?

 

In three (or more) dimensions, we find that there is a deterministic spatial

scale common to all the large gaps anywhere in the torus.  Moreover, we can

identify whether a gap of a given shape is likely to exist on this scale, in

terms of a single parameter, the classical (Newtonian) capacity.  I will

describe why this allows us to identify a well-defined "component" structure in

our random porous set.


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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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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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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.

Note for Attendees

Refreshments will be served in ESB 4133 (PIMS Lounge) at 2:45 p.m. before this colloquium.
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Federico Scavia
UBC
Mon 29 Jan 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
Essential dimension of representations of algebras
MATH 126
Mon 29 Jan 2018, 4:00pm-5:00pm

Abstract

The essential dimension of an algebraic object is the minimal number of independent parameters one needs to define it. I will explain how the representation type of a finitely-generated algebra (finite, tame, wild) is determined by the essential dimension of the functors of its n-dimensional representations and I will introduce new numerical invariants for algebras. I will then illustrate the theorem and explicitely determine the invariants in the case of quiver algebras.
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USC
Tue 30 Jan 2018, 2:00pm SPECIAL
MATH126
Teaching and Learning Mathematics: In the Classroom and Beyond
MATH126
Tue 30 Jan 2018, 2:00pm-3:00pm

Details

 
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UBC
Wed 31 Jan 2018, 3:10pm
Probability Seminar
LSK 460
The dimension of the boundary of super-Brownian motion
LSK 460
Wed 31 Jan 2018, 3:10pm-4:10pm

Abstract

 
We show that the Hausdorff dimension of the boundary of d-dimensional super-Brownian motion is 0, if d=1; 4-2^{3/2}, if d=2; and (9-17^{1/2}})/2, if d=3. This is a joint work with Leonid Mytnik. 
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University of British Columbia
Wed 31 Jan 2018, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Spherical posets from commuting elements
ESB 4133 (PIMS Lounge)
Wed 31 Jan 2018, 3:15pm-4:15pm

Abstract

Given a group G the space of n-tuples of pairwise commuting elements can be assembled into a subspace Bcom(G) of the classifying space BG. This space classifies certain types of principal bundles, but unlike BG it is not always aspherical for discrete groups.

The universal cover can be studied using posets, and when G is an extraspecial p-group, I will show that it has the homotopy type of a wedge of spheres. Extraspecial groups appear as the basic observables in quantum computation, and I will also talk about some recent applications of Bcom(G).
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Florian Patout
ENS Lyon, France
Wed 31 Jan 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127
Lineages in a mutation selection model with climate change
ESB 4127
Wed 31 Jan 2018, 3:15pm-4:00pm

Abstract

I will present a new quantitative genetic model of adaptation to a changing environment. The mathematical analysis will use small variance asymptotics introduced by Diekmann et al in 2005 to derive information on the equilibrium. The framework can handle sexual and asexual reproduction. Heuristics can be made to guess the lineages of the population inside the equilibrium, as shown by numerical simulations.
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