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 Events
Ph.D. Candidate: Benjamin Wallace
Mathematics
Fri 2 Jun 2017, 12:30pm SPECIAL
Room 207, Anthropology and Sociology Bldg. UBC
Examination: Renormalization Group Analysis of Self-Interacting Walks and Spin Systems
Room 207, Anthropology and Sociology Bldg. UBC
Fri 2 Jun 2017, 12:30pm-2:30pm

Details

ABSTRACT
The central concern of this thesis is the study of critical behaviour in models of statistical physics in the upper-critical dimension. We study a generalized n-component lattice |φ|4 model and a model of weakly self-avoiding walk with nearest-neighbour contact self-attraction on the Euclidean lattice Zd. By utilizing a supersymmetric integral representation involving boson and fermion fields, the two models are studied in a unified manner.
Our main result, which is contingent on a small coupling hypothesis, identifies the precise leading-order asymptotics of the two-point function, susceptibility, and finite-order correlation length of both models in d = 4. In particular, we show that the critical two-point function satisfies mean-field scaling whereas the near-critical susceptibility and finite-order correlation length exhibit logarithmic corrections to mean-field behaviour. The proof employs a renormalisation group method of Bauerschmidt, Brydges, and Slade based on a finite-range covariance decomposition and requires two extensions to this method.
The first extension, which is required for the computation of the finite-order correlation length (even for the ordinary weakly self-avoiding walk and |φ|4 model), is an improvement of the norms used to control the evolution of the renormalisation group. This allows us to obtain improved error estimates in the massive regime of the renormalisation group flow.
The second extension involves the identification of critical parameters for models initialized with a non-zero error coordinate coupled to a marginal/relevant coordinate. This allows us, for example, to realize the two-point function and susceptibility for the walk with self-attraction as a small perturbation of the corresponding quantities without self-attraction, whose asymptotic behaviour was determined by Bauerschmidt, Brydges, and Slade. This establishes a form of universality
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University of Washington
Mon 5 Jun 2017, 11:00am SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
MATH 126
Asymptotic behavior of solutions to Hessian equations over exterior domains
MATH 126
Mon 5 Jun 2017, 11:00am-12:00pm

Abstract

 We present a unified approach to quadratic asymptote of solutions to a class of fully nonlinear elliptic equations over exterior domains, including Monge-Ampere equations (previously known), special Lagrangian equations, quadratic Hessian equations, and inverse harmonic Hessian equations. This is joint work with Dongsheng Li and Zhisu Li.
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City of Hope Cancer Center, Duarte, California
Wed 7 Jun 2017, 1:30pm SPECIAL
Mathematical Biology Seminar
ESB 5104
Complexity of the Tumor Microenvironment
Joshua Scurll
Department of Mathematics, The University of British Columbia
Tue 13 Jun 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
StormGraph: A graph-based clustering algorithm for the analysis of super-resolution microscopy data
ESB 4133 (PIMS Lounge)
Tue 13 Jun 2017, 12:30pm-1:30pm

Abstract

With super-resolution microscopy techniques such as Direct Stochastic Optical Reconstruction Microscopy (dSTORM), it is possible to image fluorescently labeled proteins on a cell membrane with high precision. Often, the extent to which such proteins cluster is biologically meaningful; for example, in B-cells, clustering of the B-cell receptor (BCR) is associated with increased intracellular signaling and B-cell activation, and spontaneous BCR clustering can cause chronic active BCR signaling that results in an aggressive B-cell malignancy. Computational methods are therefore needed to make quantifiable comparisons between the observed clustering in different data sets, such as for different cell types or different experimental conditions.

Inspired by the success of graph-based clustering algorithms such as PhenoGraph in other research areas, we developed StormGraph, a graph-based clustering algorithm for analyzing Single Molecule Localization Microscopy (SMLM) data such as would be obtained by dSTORM.

This talk will present StormGraph, which distinguishes clusters from random background and assigns individual localizations to specific clusters, 
allowing for a detailed analysis of statistics such as cluster area. The utility of StormGraph will be illustrated on dSTORM data of BCRs imaged on malignant B-cells.
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University of Oxford
Thu 15 Jun 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Commutative complex K-theory
ESB 4133 (PIMS Lounge)
Thu 15 Jun 2017, 3:15pm-4:45pm

Abstract

The study of spaces of homomorphisms from a discrete group to a compact Lie group has led to the definition of a new cohomology theory, called commutative K-theory. This theory, which was first introduced by Adem and Gomez, is a refinement of classical topological K-theory. It is defined using vector bundles which can be represented by commuting cocycles. I will begin the talk by discussing some general properties of the "classifying space for commutativity in a Lie group". Specialising to the unitary groups, I will show that the classifying space for commutative complex K-theory is precisely the E-Infinity ring space underlying the ku-group ring of BU(1). If time permits, I will mention some results about the real variant of commutative K-theory.
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Ph.D. Candidate: Thomas Hutchcroft
Mathematics, UBC
Fri 16 Jun 2017, 12:45pm SPECIAL
Room 4127, Earth Sciences (ESB) Building, UBC
Final Oral Examination: Perspectives on some aspects of discrete probability
Room 4127, Earth Sciences (ESB) Building, UBC
Fri 16 Jun 2017, 12:45pm-2:45pm

Details

Abstract:
We prove several theorems concerning random walks, harmonic functions, percolation, uniform spanning forests, and circle packing. We study these models primarily on planar graphs and on unimodular random rooted graphs, although some of our results hold for more general classes of graphs. Broadly speaking, we are interested in the interplay between the geometry of a graph and the behaviour of probabilistic processes on that graph. Material taken from a total of nine papers is included. We have also included an extended introduction explaining the background to these papers.

Note for Attendees

Latecomers will not be admitted.
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Martin Hairer
University of Warwick
Fri 16 Jun 2017, 4:00pm SPECIAL
Department Colloquium
University of British Columbia, Earth Science Bldg. Room 1013
PIMS-UBC Distinguished Colloquium: On coin tosses, atoms, and forest fires
University of British Columbia, Earth Science Bldg. Room 1013
Fri 16 Jun 2017, 4:00pm-5:00pm

Abstract

We will survey some of the mathematical objects arising naturally in probability theory, as well as some of their surprising properties. In particular, we will see how one of these objects was involved in the confirmation of the existence of atoms over 100 years ago and how new properties of related objects are still being discovered today.


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University of Oxford
Thu 22 Jun 2017, 3:15pm
ESB 4133 (PIMS Lounge)
Commutative complex K-theory, Part II
ESB 4133 (PIMS Lounge)
Thu 22 Jun 2017, 3:15pm-4:45pm

Details

 

Last time we have seen that the spectrum for commutative K-theory is equivalent to the ku-group ring of BU(1). In this second talk I will show how this induces a splitting of the space BcomU as a product of all the stages in the Whitehead tower for BU. I will then explain the relationship between the homotopy groups of BcomU and certain rational characteristic classes introduced by Adem and Gómez. Finally, I would like to explain an alternative but equivalent picture using Segal's Dold-Thom functor for K-homology theory.

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Altius Institute for Biomedical Sciences. Seattle, WA
Wed 28 Jun 2017, 1:30pm
Mathematical Biology Seminar
MATH 126
Statistical learning models to identify the ingredients of enhancer-responsive gene promoters
 
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