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 Events
Jay Newby
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, 3:30pm-4:30pm

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.

Note for Attendees

A light reception will be served at the PIMS Lounge, 4133 from  3:00pm.
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Jay Newby
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, 12:00pm-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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Henri Darmon
McGill University
Fri 2 Feb 2018, 3:30pm
PIMS Seminars and PDF Colloquiums
ESB 2012
PIMS-CRM-FIELDS Prize Lecture: Modular functions, modular cocycles, and the arithmetic of real quadratic fields
ESB 2012
Fri 2 Feb 2018, 3:30pm-4:30pm

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 p-adic 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 p-modular 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 Coxeter-James 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.

Note for Attendees

Refreshments will be served from 3:00pm at the PIMS Lounge: ESB 4133.
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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, 4:00pm-5:00pm

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, 4:00pm-5:00pm

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 d-1. 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 d-1". 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 d-1. Additionally, this isomorphism is unique up to subsets of dimension at most d-1. 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 d-1"} x {"line bundles on X up to subsets dimension d-1"}.
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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, 2:00pm-3:00pm

Details


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Indiana University
Tue 6 Feb 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
The Monge-Ampere eigenvalue problem, Brunn-Minkowski inequality and global smoothness of the eigenfunctions
ESB 2012
Tue 6 Feb 2018, 3:30pm-4:30pm

Abstract

In this talk, I will first introduce the Monge-Ampere eigenvalue problem on general bounded convex domains and related analysis including the Brunn-Minkowski 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 Monge-Ampere operator on smooth, bounded and uniformly convex domains in all dimensions. A key ingredient in our analysis is boundary Schauder estimates for certain degenerate Monge-Ampere 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, 3:10pm-4:10pm

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 tree-valued 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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Kieran Campbell
UBC Stats
Wed 7 Feb 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127
Bayesian latent variable models for understanding (pseudo-) time-series single-cell gene expression data
ESB 4127
Wed 7 Feb 2018, 3:15pm-4:15pm

Abstract

In the past five years biotechnological innovations have enabled the measurement of transcriptome-wide gene expression in single-cells. However, the destructive nature of the measurement process precludes genuine time-series 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 re-casting 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 covariate-adjusted 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, 2:00pm-3:00pm

Details


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Ray Walsh
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, 12:30pm-1:30pm

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 two-dimensional 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, 2:00pm-3:00pm

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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, 4:00pm-5:00pm

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 order-siomorphic 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 cycle-free 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 3-spheres
ESB 4133
Wed 14 Feb 2018, 3:15pm-4:15pm

Abstract

 We use methods from the cohomology of groups to describe the finite groups which can act freely and homologically trivially on closed 3-manifolds which are rational homology spheres. This is joint work with I. Hambleton.
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Andreas Buttenschoen
UBC, Math
Wed 14 Feb 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127
Integro-partial differential equation models for cell-cell adhesion and its application
ESB 4127
Wed 14 Feb 2018, 3:15pm-4:15pm

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 integro-partial differential equation (iPDE) model. The initial success of the model was the replication of the cell-sorting 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 non-local (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 cell-size of density of adhesion molecules affect tissue level phenomena. I will also present a study of the steady-states of the non-local cell adhesion model on an interval with periodic boundary conditions. The importance of steady-states is that these are the patterns observed in nature and tissues (e.g. cell-sorting experiments). I combine global bifurcation results pioneered by Rabinowitz, equivariant bifurcation theory, and the mathematical properties of the non-local term to obtain a global bifurcation result for the first branch of non-trivial solutions. I will extend the non-local cell adhesion model to a bounded domain with no-flux boundary conditions.
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Tommi Muller
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, 3:15pm-4:15pm

Abstract

The dynamics of the T immune cell membrane and the motion of its surface-bound receptors can be analyzed using a sophisticated microscopy technique called Total Internal Reflection Fluorescence Microscopy (TIRF), where receptors can be tagged with light-emitting particles that are illuminated by a laser. Methods in probability and numerical analysis, such as the Finite-State Hidden Markov Model and the Metropolis-Hastings algorithm, were applied to the trajectories of the receptors from the microscopy images using single-particle 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 Finite-State 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/under-fitting data and cherry-picking data. In this presentation, we will explore TIRF, the Metropolis-Hastings 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 infinite-sized 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, 3:00pm-4:00pm

Abstract

The Szemerédi-Trotter 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, 3:00pm-4:00pm

Abstract

Leveraging physical contacts to interact with our surroundings is an essential skill to achieve any physical task, but contact-rich, 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 pick-and-place 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 non-differentiability 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 model-based approach to controlling a deformable robot for locomotion. The control algorithm leverages both static and dynamic contact friction by solving an optimization with non-differentiable linear complementarity constraints efficiently. The second part of the talk focuses on a model-free 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 data-driven haptic perception for robot-assisted dressing tasks.

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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SFU
Mon 26 Feb 2018, 4:00pm SPECIAL
Algebraic Geometry Seminar
MATX 1118
Fujita's Freeness Conjecture for Complexity-One T-Varieties
MATX 1118
Mon 26 Feb 2018, 4:00pm-5:00pm

Abstract

Fujita famously conjectured that for a d-dimensional 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 d-1.
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Tyrone Rees
STFC Rutherford Appleton Laboratory, UK
Tue 27 Feb 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Nonlinear least-squares problems: a second look
ESB 4133 (PIMS Lounge)
Tue 27 Feb 2018, 12:30pm-1:30pm

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 least-squares problem. Standard methods for solving such problems are based on the Gauss-Newton and Newton approximation, solved either within a trust-region or with an additional regularization term (e.g., the Levenberg-Marquardt method).   

I will describe a method that combines Gauss-Newton and Newton approximations, where appropriate, to produce a hybrid method that exhibits better convergence properties. I will then describe a newly proposed algorithm, the tensor-Newton method, that minimizes a tensor model locally. Since this shares the sum-of- 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 real-world 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 least-squares 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, 3:10pm-4:10pm

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 n-element 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 1/2-way permutation matrix measure converges to the projected surface area measure of the 2-sphere.
 
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
 
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