Mathematics Dept.
  Events
Eberhard Karls University, Tuebingen
Tue 3 Apr 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Edge universality in interacting topological insulators
ESB 2012
Tue 3 Apr 2018, 3:30pm-4:30pm

Abstract

In this talk, I will present universality results for the edge transport properties of interacting, 2d topological insulators. I will mostly focus on the case of quantum Hall systems, displaying single mode edge currents. After reviewing recent results for the bulk transport properties, I will present a theorem establishing the universality of the edge conductance and the emergence of spin-charge separation for the edge modes. Combined with well-known results for noninteracting systems, our theorem implies the validity of the bulk-edge correspondence for a class of weakly interacting 2d lattice models, including for instance the interacting Haldane model. The proof is based on rigorous renormalization group methods, and on the combination of chiral Ward identities for the effective 1d QFT describing the infrared scaling limit of the edge currents, together with lattice Ward identities for the original lattice model. Joint work with G. Antinucci (UZH/Tuebingen) and with V. Mastropietro (Milan).
hide
University of Washington
Wed 4 Apr 2018, 3:10pm
Probability Seminar
LSK 460
The spectral gap in bipartite biregular graphs
LSK 460
Wed 4 Apr 2018, 3:10pm-4:10pm

Abstract

 

The asymptotics of the second-largest eigenvalue in random regular graphs (also referred to as the Alon conjecture) have been computed by Joel Friedman in his celebrated 2004 paper. Recently, a new proof of this result has been given by Charles Bordenave, using the non-backtracking operator and the Ihara-Bass formula. In the same spirit, we have been able to translate Bordenave's ideas to bipartite biregular graphs in order to calculate the asymptotical value of the second-largest pair of eigenvalues, and obtained a similar spectral gap result. Applications include community detection in equitable graphs or frames, matrix completion, and the construction of channels for efficient and tractable error-correcting codes (Tanner codes). This work is joint with Gerandy Brito and Kameron Harris.


hide
Josh Scurll
UBC, Math
Wed 4 Apr 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127
Building a pipeline to study proteomic heterogeneity in B-cell lymphomas using mass cytometry.
ESB 4127
Wed 4 Apr 2018, 3:15pm-4:15pm

Abstract

Diffuse Large B-Cell Lymphoma (DLBCL), a non-Hodgkin lymphoma, is the most common blood cancer and comprises more than two subtypes. The Activated B-Cell like (ABC) subtype has inferior survival rates, and is typically characterized by constitutive signalling that resembles B-cell activation following antigen engagement. However, there is significant heterogeneity observed clinically within the ABC subtype of DLBCL, with various mutations able to give rise to this oncogenic  signalling. When present within an individual patient's tumour, this kind of heterogeneity can lead to drug resistance due to evolutionary selection for cells with mutations that confer drug resistance. Optimized personalized therapies should therefore  account for any underlying intratumour heterogeneity to prevent or delay the onset of drug resistance. In this work-in-progress talk, I will present our work towards developing a pipeline using mass cytometry -- a technique that enables the measurement of over 30 proteins simultaneously in single cells -- and computational analysis to study proteomic heterogeneity, especially at the level of intracellular signalling, in DLBCL samples. Since the 'ground-truth' cellular populations (clusters in proteomic or mutational feature space) that make up a heterogeneous tumour are not known for real tumours, we have devised novel mass cytometry experiments to simulate a heterogeneous DLBCL sample using cell lines as 'ground truth' populations. This novel data will facilitate the improvement of existing, and development of new, computational algorithms for analysing heterogeneity and signalling in tumours.
hide
University of British Columbia
Wed 4 Apr 2018, 3:15pm
Topology and related seminars
ESB 4133
The role of contextuality for quantum computation
ESB 4133
Wed 4 Apr 2018, 3:15pm-4:15pm

Abstract

 Contextuality is a property of quantum mechanics that sets it apart from classical physics. Recently, it has been established as a necessary ingredient that any quantum computation must have in order to provide a speedup over conventional classical computation [1], [2]. It has thus become a resource.

In my talk, I will first review the notion of quantum contextuality, and then explain how it is a useful commodity in quantum computation---for the models of quantum computation with magic states and measurement-based quantum computation (MBQC). 

I’ll end with a cohomological picture underlying MBQC and contextuality [3], which is a focus of current research in my group.

[1] M. Howard et al., Nature (London) 510, 351 (2014).

[2] R. Raussendorf, Phys. Rev. A 88, 022322 (2013).

[3] C. Okay et al., Quantum Information and Computation 17, 1135-1166 (2017).

hide
Oxford
Thu 5 Apr 2018, 4:00pm SPECIAL
Algebraic Geometry Seminar
MATH 126
Hyperkahler implosion
MATH 126
Thu 5 Apr 2018, 4:00pm-5:00pm

Abstract

Abstract: The hyperkahler quotient construction (introduced by Hitchin
et al in the 1980s) allows us to construct new hyperkahler spaces from
suitable group actions on hyperkahler manifolds. This construction is an
analogue of symplectic reduction (introduced by Marsden and Weinstein in
the 1970s), and both are closely related to the quotient construction
for complex reductive group actions in algebraic geometry provided by
Mumford's geometric invariant theory (GIT). Hyperkahler implosion is in
turn an analogue of symplectic implosion (introduced in a 2002 paper of
Guillemin, Jeffrey and Sjamaar) which is related to a generalised
version of GIT providing quotients for non-reductive group actions in
algebraic geometry.
hide
University of Oxford
Fri 6 Apr 2018, 3:00pm
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium: Moduli spaces of unstable curves
ESB 2012
Fri 6 Apr 2018, 3:00pm-4:00pm

Abstract

  Moduli spaces arise naturally in classification problems in geometry. The study of the moduli spaces of nonsingular complex projective curves (or equivalently of compact Riemann surfaces) goes back to Riemann himself in the nineteenth century. The construction of the moduli spaces of stable curves of fixed genus is one of the classical applications of Mumford's geometric invariant theory (GIT), developed in the 1960s. Here a projective curve is stable if it has only nodes as singularities and its automorphism group is finite. The aim of this talk is to describe these moduli spaces and outline their GIT construction, and then explain how recent methods from non-reductive GIT can help us to classify the singularities of unstable curves in such a way that we can construct moduli spaces of unstable curves (of fixed singularity type).

Note for Attendees

Light refreshments will be served at 2:45pm in ESB 4133, the PIMS Lounge before this colloquium.
hide
Luca Martinazzi
Univ. Padova
Tue 10 Apr 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
MATH 225 **Special**
News on the Moser-Trudinger inequality: from sharp estimates to the Leray-Schauder degree
MATH 225 **Special**
Tue 10 Apr 2018, 3:30pm-4:30pm

Abstract

The existence of critical points for the Moser-Trudinger inequality for large energies has been open for a long time. We will first show how a collaboration with G. Mancini allows to recast the Moser-Trudinger inequality and the existence of its extremals (originally due to L. Carleson and A. Chang) under a new light, based on sharp energy estimate. Building upon a recent subtle work of O. Druet and P-D. Thizy, in a work in progress with O. Druet, A. Malchiodi and P-D. Thizy, we use these estimates to compute the Leray-Schauder degree of the Moser-Trudinger equation (via a suitable use of the Poincaré-Hopf theorem), hence proving that for any bounded non-simply connected domain the Moser-Trudinger inequality admits critical points of arbitrarily high energy.



 
hide
Felix Funk
UBC, Math
Wed 11 Apr 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127
The Impact of Directed Movement on Ecological Public Goods Interactions
ESB 4127
Wed 11 Apr 2018, 3:15pm-4:15pm

Abstract

Frequently, the interests of a group do not align with those of its members. An individual could, for instance, do well by considering the collective needs in its actions but many times, it can gain even more benefits within the group by pursuing personal interests to the detriment of the entire community. This social dilemma is at the heart of public good interactions, and of particular importance when the production of a public resource is essential for the survival of a population. This scenario occurs, for example, when microbes secrete substances which grant microbial communities resistance to antibiotic drugs.

The arising dynamics for the public good producing cooperative and the freeriding non-cooperative subpopulations have previously been analyzed by Professor Hauert and Professor Doebeli and extended by Wakano et al. into a spatial setting, in which the diffusing microbes form clusters and showcase rich patterns. As many microbes sense chemical gradients - and with that the public good - directional movement can lead to the aggregation of cooperative clusters and the exploitation through the defective subpopulation alike. In this talk, I will incorporate chemotactic migration in the aforementioned models and discuss how this extension affects the composition of the subpopulation, and whether cooperation can be maintained.

This talk also showcases some parts of my research that are still in progress, and I'm happy to hear your feedback.
hide
Duke University
Thu 12 Apr 2018, 3:30pm
Number Theory Seminar
Math 126
Summation formulae and speculations on period integrals attached to triples of automorphic representations
Math 126
Thu 12 Apr 2018, 3:30pm-5:00pm

Abstract

Braverman and Kazhdan have conjectured the existence of summation formulae that are essentially equivalent to the analytic continuation and functional equation of Langlands L-functions in great generality.  Motivated by their conjectures and related conjectures of L. Lafforgue, Ngo, and Sakellaridis, Baiying Liu and I have proven a summation formula analogous to the Poisson summation formula for the subscheme cut out of three quadratic spaces (V_i,Q_i) of even dimension by the equation

Q_1(v_1)=Q_2(v_2)=Q_3(V_3).

I will sketch the proof of this formula in the first portion of the talk.  In the second portion, time permitting, I will discuss how these summation formulae lead to functional equations for period integrals for automorphic representations of

GL_{n_1} \times GL_{n_2} \times GL_{n_3}

where the n_i are arbitrary, and speculate on the relationship between these period integrals and Langlands L functions.
hide
PhD Candidate: Hildur Knutsdottir
Mathematics, UBC
Fri 13 Apr 2018, 9:00am SPECIAL
Room 126, MATH Bldg., 1984 Mathematics Road, UBC
Exam: The Multi-levelled Organization of Cell Migration: From Individual Cells to Tissues
Room 126, MATH Bldg., 1984 Mathematics Road, UBC
Fri 13 Apr 2018, 9:00am-11:00am

Details

Abstract:
Cell migration is a complex interplay of biochemical and biophysical mechanisms. I investigate the link between individual and collective cell behaviour using mathematical and computational modelling. Specifically, I study: (1) cell-cell interactions in a discrete framework with a spatial sensing range, (2) migration of a cluster of cells during zebrafish (Danio rerio) development, and (3) collective migration of cancer cells and their interactions with the extracellular-matrix (ECM).

My 1D model (1), is approximated by a continuum equation and investigated using asymptotic approximations, steady-state analysis, and linear stability analysis. Analysis and computations characterize regimes corresponding to cell clustering, and provide a link between micro and macro-scale parameters. Results suggest that drift (i.e. due to chemotaxis), can disrupt the formation of cellular aggregates.

In (2), I investigate spontaneous polarization of a cell-cluster (the posterior lateral line primordium, PLLP) in zebrafish development. I use a cell-based computational framework (HyDiCell3D) coupled with a differential equation model to track the segregation and migration of the PLLP. My model includes mutual inhibition between the diffusible growth factors Wnt and FGF. I find that a non-uniform degradation of an extracellular chemokine (CXCL12a) and chemotaxis is essential for long range cohesive migration. Results compare favourably with data from the Chitnis lab (NIH).

I continue using HyDiCell3D in (3) to elucidate mechanisms that facilitate cancer invasion. I focus on: wound healing in a cell-sheet (2D epithelium), and cell-clusters (3D spheroids) embedded in ECM with internal signalling mediated by podocalyxin, a trans-membrane molecule. Experimental data from the Roskelley lab (UBC) motivates the model derivation. I use the models to investigate the role of cell-cell and cell-ECM adhesion in collective migration as well as the emergence of a distinct phenotype (leader-cells) that guides the migration. ECM induced disruption in the localization of podocalyxin on the cell membrane is captured in the model along with morphological changes of spheroids. The model predicts that cell polarity and cell division axis influence the invasive potential. Lastly, I develop quantitative methods for image analysis and automated tracking of cells in a densely packed environment to compare modelling results and biological data.

Note for Attendees

Latecomers will not be admitted.
hide
Zhifei Zhu
University of Toronto
Tue 17 Apr 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Geometric Inequalities on Riemannian manifolds
ESB 2012
Tue 17 Apr 2018, 3:30pm-4:30pm

Abstract

I will discuss some upper bounds for the length of a shortest periodic geodesic, and the smallest area of a closed minimal surface on closed Riemannian manifolds of dimension 4 with Ricci curvature between -1 and 1. These are the first bounds that use information about the Ricci curvature rather than sectional curvature of the manifold. (Joint with Nan Wu).

I will also give examples of Riemannian metrics on the 3-disk demonstrating that the maximal area of 2-spheres arising during  an ``optimal" homotopy contracting its boundary cannot be majorized  in terms of the volume and diameter of the 3-disc and the area of its boundary. This contrasts with earlier 2-dimensional results of Y. Liokomovich, A. Nabutovsky and R. Rotman and answers a question of P. Papasoglu. On the other hand I will show that such an upper bound exists if, instead of the  volume, one is allowed to use the first homological filing function of the 3-disc. (Joint with Parker Glynn-Adey).

hide
Ohio State University
Wed 18 Apr 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127
A bundled approach for high-dimensional informatics problems
ESB 4127
Wed 18 Apr 2018, 3:15pm-4:15pm

Abstract

As biotechnologies for data collection become more efficient and mathematical modeling becomes more ubiquitous in the life sciences, analyzing both high-dimensional experimental measurements and high-dimensional spaces for model parameters is of the utmost importance. We present a perspective inspired by differential geometry that allows for the exploration of complex datasets such as these. In the case of single-cell leukemia data we present a novel statistic for testing differential biomarker correlations across patients and within specific cell phenotypes. A key innovation here is that the statistic is agnostic to the clustering of single cells and can be used in a wide variety of situations. Finally, we consider a case in which the data of interest are parameter sets for a nonlinear model of signal transduction and present an approach for clustering the model dynamics. We motivate how the aforementioned perspective can be used to avoid global bifurcation analysis and consider how parameter sets with distinct dynamic clusters contrast.
hide
Lisanne Rens
UBC, Math
Wed 25 Apr 2018, 3:15pm
Mathematical Biology Seminar
ESB 4127
Mathematical biology of cell-extracellular matrix interactions during morphogenesis
ESB 4127
Wed 25 Apr 2018, 3:15pm-4:15pm

Abstract

Morphogenesis, the shaping of organisms, organs and tissues is driven by chemical signals and physical forces. It is still poorly understood how cells are able to collectively form intricate patterns, like for instance vascular networks. In particular, we were concerned with how interactions between the cell and the extracellular matrix (a protein network surrounding tissues that supports cells and guides cell migration) regulates morphogenesis. My PhD has mainly focused on how physical forces may drive morphogenesis. Lab experiments have shown that the mechanical properties of the matrix, such as its stiffness, regulate morphogenesis. In this presentation I will focus on my work on mechanical cell-matrix interactions. We developed a multiscale model that describe cells and the matrix and their interactions through physical forces. In this model, cells are represented by the Cellular Potts Model. The deformations in the ECM are calculated using a Finite Element Method. We model a mechanical feedback between cells and the ECM, where 1) cells pull on the ECM, 2) strains are generated in the ECM, and 3) cells preferentially extend protrusions oriented with strain. Similar to lab experiments, simulations show that cells are able to generate vascular like patterns on matrices of intermediate stiffness. Lab experiments where the matrix is uniaxially stretched, show that cells orient parallel to stretch. Model results on cells on a stretched matrices with and without traction forces indicate that cell traction forces amplify cell orientation parallel to stretch. Furthermore, they allow cells to organize into strings in the direction of stretch. I will also show an extension of this model. Stiffness sensing is mediated by transmembrane integrin molecules, which behave as ‘catch bonds’ whose strength increases under tension. Focal adhesions, which are large assemblies of these integrins, grow larger on stiffer substrates. We included such dynamics in our multiscale model. This second model explains how cell shape depends on matrix stiffness and how cells are able to durotact (move up a stiffness gradient). This model gives a more molecular understanding of how cells respond to matrix stiffness. 
hide