Univ. of North Carolina Chapel Hill

Thu 1 Feb 2018, 3:30pm
Department Colloquium
ESB 2012

Weaker is better: how weak transient molecular interactions give rise to robust, dynamic immune protection

ESB 2012
Thu 1 Feb 2018, 3:30pm4:30pm
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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Univ. of North Carolina Chapel Hill

Fri 2 Feb 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
Fri 2 Feb 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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McGill University

Fri 2 Feb 2018, 3:30pm
PIMS Seminars and PDF Colloquiums
ESB 2012

PIMSCRMFIELDS Prize Lecture: Modular functions, modular cocycles, and the arithmetic of real quadratic fields

ESB 2012
Fri 2 Feb 2018, 3:30pm4:30pm
Abstract
Modular functions play an important role in many aspects of number theory. The theory of complex multiplication, one of the grand achievements of the subject in the 19th century, asserts that the values of modular functions at quadratic imaginary arguments generate (essentially all) abelian extensions of imaginary quadratic fields. Kronecker's famous ``Jugendtraum", which later came to be known as Hilbert’s twelfth problem concerns the generalization of this theory to other base fields. I will describe an ongoing work in collaboration with Jan Vonk which identifies a class of functions that seem to play the role of modular functions for real quadratic fields. A key difference with the classical setting is that they are meromorphic functions of a padic variable (defined in the framework of “rigid analysis” introduced by Tate) rather than of a complex variable. An important role in this theory of ``rigid modular cocycles" is played by the pmodular group {\bf SL}_2({\rm bf Z}[1/p]) whose cohomology was studied by Serre and Adem.
Biography
Born in 1965 in Paris, France, Darmon moved to Canada in 1968. He received a bachelor's degree from McGill University in 1987 and a PhD in mathematics from Harvard University in 1991, under the supervision of Benedict Gross. He then held a postdoctoral position at Princeton University, under the mentorship of Andrew Wiles. It was around this time that Wiles gained worldwide fame for his proof of Fermat's Last Theorem.
In 1994, Darmon joined the faculty of McGill University, where he is currently a James McGill Professor in the Department of Mathematics and Statistics. His other honors include the André Aisenstadt Prize (1997), the CoxeterJames Prize of the Canadian Mathematical Society (1998), the Ribenboim Prize of the Canadian Number Theory Association (2002), and the John L. Synge Award of the Royal Society of Canada (2008). He was elected a Fellow of the Royal Society of Canada in 2003 and received the 2017 AMS Cole Prize in Number Theory for his contributions to the arithmetic of elliptic curves and modular forms.
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UBC

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

Motivic classes of algebraic groups

MATH 126
Sun 4 Feb 2018, 4:00pm5:00pm
Abstract
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UBC

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

A birational Gabriel's theorem (joint w/ J. Calabrese).

MATH 126
Mon 5 Feb 2018, 4:00pm5:00pm
Abstract
A famous theorem by Gabriel asserts that two Noetherian schemes X, Y are isomorphic if and only if the categories Coh(X), Coh(Y) are isomorphic. This theorem has been extended in many directions, including algebraic spaces and stacks (if we consider the monoid structure given by tensor product). One more idea to extend the theorem is the following: let X be a scheme of finite type over a field k, and consider the subcategory of Coh(X) given by sheaves supported in dimension at most d1. We can form the quotient of Coh(X) by this subcategory, which we will call C_d(X). This category should contain enough information to describe the geometry of X "up to subsets of dimension d1". In a joint work in progress with John Calabrese, we show that this is indeed true, i.e. to any isomorphism f: C_d(Y) > C_d(X) we can associate an isomorphism f': U> V, where U and V are open subset respectively of X and Y whose complement have dimension at most d1. Additionally, this isomorphism is unique up to subsets of dimension at most d1. As a corollary of this result, we show that the automorphisms of C_d(X) are in bijection with the set {"automorphisms of X up to subsets of dimension d1"} x {"line bundles on X up to subsets dimension d1"}.
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Harvard

Tue 6 Feb 2018, 2:00pm
SPECIAL
MATH 225

My vision of teaching and learning: connecting the minds

MATH 225
Tue 6 Feb 2018, 2:00pm3:00pm
Details
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Indiana University

Tue 6 Feb 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

The MongeAmpere eigenvalue problem, BrunnMinkowski inequality and global smoothness of the eigenfunctions

ESB 2012
Tue 6 Feb 2018, 3:30pm4:30pm
Abstract
In this talk, I will first introduce the MongeAmpere eigenvalue problem on general bounded convex domains and related analysis including the BrunnMinkowski inequality for the eigenvalue. Then I will discuss the recent resolution, in joint work with Ovidiu Savin, of global smoothness of the eigenfunctions of the MongeAmpere operator on smooth, bounded and uniformly convex domains in all dimensions. A key ingredient in our analysis is boundary Schauder estimates for certain degenerate MongeAmpere equations.
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University of Washington

Wed 7 Feb 2018, 3:10pm
Probability Seminar
LSK 460

Random walks on a space of trees with integer edge weights

LSK 460
Wed 7 Feb 2018, 3:10pm4:10pm
Abstract
Consider the Markov process in the space of binary trees in which, at each step, you delete a random leaf and then grow a new leaf in a random location on the tree. In 2000, Aldous conjectured that it should have a continuum analogue, which would be a continuum random treevalued diffusion. We will discuss a family of projectively consistent Markov chains that are projections of this tree, and discuss how these representations can be passed to the continuum. This is joint work with Soumik Pal, Douglas Rizzolo, and Matthias Winkel.
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UBC Stats

Wed 7 Feb 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127

Bayesian latent variable models for understanding (pseudo) timeseries singlecell gene expression data

ESB 4127
Wed 7 Feb 2018, 3:15pm4:15pm
Abstract
In the past five years biotechnological innovations have enabled the measurement of transcriptomewide gene expression in singlecells. However, the destructive nature of the measurement process precludes genuine timeseries analysis of e.g. differentiating cells. This has led to the pseudo time estimation (or cell ordering) problem: given static gene expression measurements alone, can we (approximately) infer the developmental progression (or "pseudotime") of each cell? In this talk I will introduce the problem from the typical perspective of manifold learning before recasting it as a (Bayesian) latent variable problem. I will discuss approaches including nonlinear factor analysis and Gaussian Process Latent Variable Models, before introducing a new class of covariateadjusted latent variable models that can infer such pseudotimes in the presence of heterogeneous environmental and genetic backgrounds.
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Penn State

Thu 8 Feb 2018, 2:00pm
SPECIAL
MATH 126

Alternatives to the Standard Calculus Curriculum

MATH 126
Thu 8 Feb 2018, 2:00pm3:00pm
Details
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Department of Mathematics, SFU

Tue 13 Feb 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

A Free Boundary Approach to Modelling Cloud Edge Dynamics

ESB 4133 (PIMS Lounge)
Tue 13 Feb 2018, 12:30pm1:30pm
Abstract
Much is known about cloud formation and their behaviour at large scales (kilometers). Considerably less, in atmospheric science, addresses the fluid mechanics dictating smaller scale motions that determine the shapes of cloud edges. Only recently (2015) has the mechanism for the formation of a holepunch cloud been understood; a curious phenomena whereby a growing circular hole in a shallow cloud layer opens up due to a disturbance typically initiated via aircraft. We present a twodimensional thermodynamic model for the edge motion of a convectively stable cloud under thermodynamic conditions that are near saturation. The proposed model couples stratified fluid mechanics through the Boussinesq equations linked to the theory of moist thermodynamics. This leads to a free boundary model for an interface separating clear and cloudy air. The presence of the two phases of moist air (clear/cloudy) induces derivative discontinuities across the boundary. We are adapting the immersed interface method (IIM), a finite difference approach, to compute the Poisson inversion for pressure to second order accuracy. We then demonstrate the application of this IIM approach to motions of the top of a fog layer. It is confirmed that a propagating wave on the clear/fog interface obeys a gravity wave dispersion relation.
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UBC

Tue 13 Feb 2018, 2:00pm
SPECIAL
MATH 225

Teaching mathematics and building communities

MATH 225
Tue 13 Feb 2018, 2:00pm3:00pm
Details
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Rényi Institute

Tue 13 Feb 2018, 4:00pm
Discrete Math Seminar
ESB 4127

Extremal graph theory of ordered graphs

ESB 4127
Tue 13 Feb 2018, 4:00pm5:00pm
Abstract
An ordered graph is simple graph with a linearly ordered vertex set. The Turán type extremal theory can be extended to ordered graph by forbidding the appearance of an ordered graph as a subgraph: we ask for the maximal number of edges in an ordered graph having no subgraph ordersiomorphic to a given pattern.
Some of the classical results of Turán type extremal graph theory carry over to this setting, while others lead to hard questions. In this talk I survey old and recent results in the area.
Here is my favorite conjecture: If the forbidden pattern is a cyclefree ordered graph which is bipartite with one partite class preceding the other, then the corresponding extremal function (the maximal number of edges of an n vertex ordered graph without this as a subgraph) is o(n^c) for any c>1. This has been proven for a large class of forbidden patterns (joint work with Dániel Korándi, István Thomon and Craig Weidert), but it is open in general and in particular it is also open for a particular ordered path on 8 vertices.
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University of British Columbia

Wed 14 Feb 2018, 3:15pm
Topology and related seminars
ESB 4133

Free finite group actions on rational homology 3spheres

ESB 4133
Wed 14 Feb 2018, 3:15pm4:15pm
Abstract
We use methods from the cohomology of groups to describe the finite groups which can act freely and homologically trivially on closed 3manifolds which are rational homology spheres. This is joint work with I. Hambleton.
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UBC, Math

Wed 14 Feb 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127

Integropartial differential equation models for cellcell adhesion and its application

ESB 4127
Wed 14 Feb 2018, 3:15pm4:15pm
Abstract
In both health and disease, cells interact with one another through cellular adhesions. Normal development, wound healing, and metastasis all depend on these interactions. These phenomena are commonly studied using continuum models (partial differential equations). However, a mathematical description of cell adhesion in such tissue models had remained a challenge until 2006, when Armstrong et. al. proposed the use of an integropartial differential equation (iPDE) model. The initial success of the model was the replication of the cellsorting experiments of Steinberg. Since then this approach has proven popular in applications to embryogenesis, wound healing, and cancer cell invasions. In this talk, I present a first derivation of the nonlocal (iPDE) model from an individual description of cell movement. The key to the derivation is the extension of the biological concept of a cell's polarization vector to the mathematical world. This derivation allows me to elucidate in detail how cell level properties such as cellsize of density of adhesion molecules affect tissue level phenomena. I will also present a study of the steadystates of the nonlocal cell adhesion model on an interval with periodic boundary conditions. The importance of steadystates is that these are the patterns observed in nature and tissues (e.g. cellsorting experiments). I combine global bifurcation results pioneered by Rabinowitz, equivariant bifurcation theory, and the mathematical properties of the nonlocal term to obtain a global bifurcation result for the first branch of nontrivial solutions. I will extend the nonlocal cell adhesion model to a bounded domain with noflux boundary conditions.
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UBC

Wed 21 Feb 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127

Embarrassingly Parallel, Infinite Chains: Reducing computational complexity to analyze T immune cell membrane receptor kinetics and generalizing the Hidden Markov Model

ESB 4127
Wed 21 Feb 2018, 3:15pm4:15pm
Abstract
The dynamics of the T immune cell membrane and the motion of its surfacebound receptors can be analyzed using a sophisticated microscopy technique called Total Internal Reflection Fluorescence Microscopy (TIRF), where receptors can be tagged with lightemitting particles that are illuminated by a laser. Methods in probability and numerical analysis, such as the FiniteState Hidden Markov Model and the MetropolisHastings algorithm, were applied to the trajectories of the receptors from the microscopy images using singleparticle tracking to estimate parameters such the diffusivity and Markov state transition probabilities of the receptors. This, however, is very computationally expensive, taking days on a supercomputer for the data analysis to complete. There is also another issue involving the FiniteState Hidden Markov Model: Before applying the model, the user must first choose and fix the number of states to model in the system. This is a significant limitation as it disables the model from adjusting to new data and it increases the possibility of over/underfitting data and cherrypicking data. In this presentation, we will explore TIRF, the MetropolisHastings Algorithm, and an approach to reduce computation time: an Embarrassingly Parallel Monte Carlo Markov Chain (MCMC) heuristic. We will also discuss the potential of using the newly developed Infinite Hidden Markov Model, which aims to overcome the limitation of fixing a finite number of states by allowing an arbitrary number of states to dynamically model data, chosen from an infinitesized state space.
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University of Bristol

Mon 26 Feb 2018, 3:00pm
Discrete Math Seminar
MATX 1101

Incidences in arbitrary fields

MATX 1101
Mon 26 Feb 2018, 3:00pm4:00pm
Abstract
The SzemerédiTrotter theorem gives a sharp upper bound on the maximum number of incidences between any finite sets of points and lines living in the real plane; this has also been extended to the complex plane. We can also ask for such an incidence bound over arbitrary fields. I will talk about two results in this direction in work joint with Frank de Zeeuw. The study of incidence bounds over the reals has found many applications in additive combinatorics; in arbitrary fields this utility remains true, and I shall present some of these applications.
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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

Optimizing physical contacts for locomotion and manipulation: turning the challenges of contacts into solutions.

ESB 2012
Mon 26 Feb 2018, 3:00pm4:00pm
Abstract
Leveraging physical contacts to interact with our surroundings is an essential skill to achieve any physical task, but contactrich, dynamically changing environments often create significant challenges to autonomous robotic locomotion and manipulation. Unexpected slippage or loss of contact can cause a balance controller to fail during locomotion, incidental contacts with unseen obstacles can disrupt a manipulator during a pickandplace task, and large impulse induced by contacts can result in irreparable damage to the robot hardware. While there exists computationally tractable contact models to aid the development of robust contro policies, the discontinuities inherent in the contact phenomenon introduce nondifferentiability in the equations of motion, rendering traditional approaches to optimal control ineffective. In this talk, I will show that, with intelligent contact control and planning algorithms, the challenge of handling contact can become a solution. The first part of the talk focuses on a modelbased approach to controlling a deformable robot for locomotion. The control algorithm leverages both static and dynamic contact friction by solving an optimization with nondifferentiable linear complementarity constraints efficiently. The second part of the talk focuses on a modelfree reinforcement learning approach to minimizing the damage of humanoid falls. We formulate the control problem as a Markov Decision Process that solves for a contact sequence with the ground such that the maximal impulse incurred during the fall is minimized. Lastly, I will mention some work we have done in the area of datadriven haptic perception for robotassisted dressing tasks.
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SFU

Mon 26 Feb 2018, 4:00pm
SPECIAL
Algebraic Geometry Seminar
MATX 1118

Fujita's Freeness Conjecture for ComplexityOne TVarieties

MATX 1118
Mon 26 Feb 2018, 4:00pm5:00pm
Abstract
Fujita famously conjectured that for a ddimensional smooth projective variety X with ample divisor H, mH+K_X is basepoint free whenever m\geq d+1. I will discuss recent joint work with Klaus Altmann in which we show this conjecture is true whenever X admits an effective action by a torus of dimension d1.
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STFC Rutherford Appleton Laboratory, UK

Tue 27 Feb 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Nonlinear leastsquares problems: a second look

ESB 4133 (PIMS Lounge)
Tue 27 Feb 2018, 12:30pm1:30pm
Abstract
One of the central problems in computational mathematics is to fit a suitable model to observed data. Mathematically, this can be posed as a nonlinear leastsquares problem. Standard methods for solving such problems are based on the GaussNewton and Newton approximation, solved either within a trustregion or with an additional regularization term (e.g., the LevenbergMarquardt method).
I will describe a method that combines GaussNewton and Newton approximations, where appropriate, to produce a hybrid method that exhibits better convergence properties. I will then describe a newly proposed algorithm, the tensorNewton method, that minimizes a tensor model locally. Since this shares the sumof squares nature of the problem being solved, it makes better use of second derivative information that has been computed than the traditional Newton approximation.
Part of the motivation of this work is improving the fitting capabilities of the widely used data analysis and visualization package Mantid. As well as standard test examples, I present results on realworld examples from ISIS, a pulsed neutron and muon source located at the Rutherford Appleton Laboratory. The algorithms described in this talk are available as part of the open source nonlinear leastsquares solver RALFit (https://github.com/ralna/RALFit).
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University of Toronto

Wed 28 Feb 2018, 3:10pm
Probability Seminar
LSK 460

The global limit of random sorting networks

LSK 460
Wed 28 Feb 2018, 3:10pm4:10pm
Abstract
A sorting network is a shortest path from the identity to the reverse permutation in the Cayley graph of S_n generated by adjacent transpositions. An nelement uniform random sorting network displays many striking global properties as n approaches infinity. For example, scaled trajectories of the elements 1, 2, ... n converge to sine curves and the 1/2way permutation matrix measure converges to the projected surface area measure of the 2sphere.
In this talk, I will discuss how the local structure of random sorting networks can be used to find a global limit, proving these statements and more.
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ICTS, Bangalore

Wed 28 Feb 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127

Data assimilation and parameter estimation

ESB 4127
Wed 28 Feb 2018, 3:15pm4:15pm
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Note for Attendees
A light reception will be served at the PIMS Lounge, 4133 from 3:00pm.