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 SelfInteracting Walks and Spin Systems

Room 207, Anthropology and Sociology Bldg. UBC
Fri 2 Jun 2017, 12:30pm2:30pm
Details
ABSTRACT
The central concern of this thesis is the study of critical behaviour in models of statistical physics in the uppercritical dimension. We study a generalized ncomponent lattice φ4 model and a model of weakly selfavoiding walk with nearestneighbour contact selfattraction 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 leadingorder asymptotics of the twopoint function, susceptibility, and finiteorder correlation length of both models in d = 4. In particular, we show that the critical twopoint function satisfies meanfield scaling whereas the nearcritical susceptibility and finiteorder correlation length exhibit logarithmic corrections to meanfield behaviour. The proof employs a renormalisation group method of Bauerschmidt, Brydges, and Slade based on a finiterange covariance decomposition and requires two extensions to this method.
The first extension, which is required for the computation of the finiteorder correlation length (even for the ordinary weakly selfavoiding walk and φ4 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 nonzero error coordinate coupled to a marginal/relevant coordinate. This allows us, for example, to realize the twopoint function and susceptibility for the walk with selfattraction as a small perturbation of the corresponding quantities without selfattraction, 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, 11:00am12:00pm
Abstract
We present a unified approach to quadratic asymptote of solutions to a class of fully nonlinear elliptic equations over exterior domains, including MongeAmpere 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

ESB 5104
Wed 7 Jun 2017, 1:30pm2:30pm
Abstract
Tumors consist not only of cancer cells, but also stromal and immune cells that constitute the tumor microenvironment. Clinical outcome and response to therapy depend on the complex interplay between these cell populations within the tumor microenvironment. Beyond numerical values, spatial organization of cells within tumors (and tumordraining lymph nodes) also impacts biological behavior. These can now be collectively addressed via a quantitative image analysis approach that incorporates 1) multicolor tissue staining (Opal, Perkin Elmer), 2) highresolution, automated wholeslide spectral imaging (Vectra, Perkin Elmer), 3) image analysis algorithms that utilize machinelearning to identify cell types and locations (InForm, Perkin Elmer), and 4) spatial statistical analysis to understand relationships between cell populations within tissue samples. This novel approach provides objective assessment of immunestromalcancer interactions within tumors and tumordraining lymph nodes, and data generated are of prognostic and mechanistic value.
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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 graphbased clustering algorithm for the analysis of superresolution microscopy data

ESB 4133 (PIMS Lounge)
Tue 13 Jun 2017, 12:30pm1:30pm
Abstract
With superresolution 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 Bcells, clustering of the Bcell receptor (BCR) is associated with increased intracellular signaling and Bcell activation, and spontaneous BCR clustering can cause chronic active BCR signaling that results in an aggressive Bcell 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 graphbased clustering algorithms such as PhenoGraph in other research areas, we developed StormGraph, a graphbased 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 Bcells.
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University of Oxford

Thu 15 Jun 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)

Commutative complex Ktheory

ESB 4133 (PIMS Lounge)
Thu 15 Jun 2017, 3:15pm4:45pm
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 Ktheory. This theory, which was first introduced by Adem and Gomez, is a refinement of classical topological Ktheory. 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 Ktheory is precisely the EInfinity ring space underlying the kugroup ring of BU(1). If time permits, I will mention some results about the real variant of commutative Ktheory.
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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, 12:45pm2:45pm
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.
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University of Warwick

Fri 16 Jun 2017, 4:00pm
SPECIAL
Department Colloquium
University of British Columbia, Earth Science Bldg. Room 1013

PIMSUBC Distinguished Colloquium: On coin tosses, atoms, and forest fires

University of British Columbia, Earth Science Bldg. Room 1013
Fri 16 Jun 2017, 4:00pm5:00pm
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 Ktheory, Part II

ESB 4133 (PIMS Lounge)
Thu 22 Jun 2017, 3:15pm4:45pm
Details
Last time we have seen that the spectrum for commutative Ktheory is equivalent to the kugroup 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 DoldThom functor for Khomology 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 enhancerresponsive gene promoters

MATH 126
Wed 28 Jun 2017, 1:30pm2:30pm
Abstract
A precise regulation of gene expression is required for virtually all biological processes, such as cell and tissue development or response to external stimuli. Misregulation of gene expression can lead to diseases, such as cancer. It is therefore crucial to improve our understanding of the components underlying the process of gene regulation. Enhancers are genomic regions (sequences) that act as regulatory elements by cooperating with core promoter regions to recruit the transcription machinery to drive gene expression. Recently emerged, genomewide experimental assays, such as STAPseq, aim to quantify the ability of genomic fragments to respond to an enhancer and drive the transcription of a gene. In this seminar, I will outline how statistical learning models enable us to extract biological insights from large, genomewide assays, such as STAPseq. As the vast majority of DNA sequences are unable to respond to enhancers and drive gene expression, we employ a zeroinflated model to address the challenge of many zeros in the data set. We harness convolutional neural networks (ConvNets) to automatically discover which DNA sequence motifs serve as ingredients of a responsive promoter. Our interpretable, zeroinflated, nonlinear Poisson regression model allows us to delineate minimal, core promoter properties from those that cooperate with the enhancer to modulate the level of gene expression.
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Seminar Information Pages

Note for Attendees
Latecomers will not be admitted.