Mathematics

Brauer classes in moduli problems and arithmetic: Lecture 1

Speaker: 
Nicholas Addington
Sara Frei
Date: 
Mon, Aug 2, 2021
Location: 
Online
Conference: 
PRIMA 2021 Summer School: Rational curves and moduli spaces in arithmetic geometry
Abstract: 

We cover Brauer classes, how they arise as obstructions on moduli spaces of sheaves, and how they can be used to obstruct rational points, highlighting recent links between the two.

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Environmental Escape from the Prisoner's Dilemma

Speaker: 
Jaye Sudweeks
Date: 
Wed, Jul 28, 2021
Location: 
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

During reproduction, viruses manufacture products that diffuse within the host cell. Because a virus does not have exclusive access to its own gene products, coinfection of multiple viruses allows for strategies of cooperation and defection— cooperators produce large amounts of gene product while defectors produce less product but specialize in appropriating a larger share of the common pool. Experimental data shows that, under conditions where coinfection is common, bacteriophage $\Phi$6 becomes trapped in a Prisoner’s dilemma, with defectors spreading to fixation, causing lowered population fitness. However, these experiments did not allow for fluctuation in the density of the external viral population. Here, I’ll discuss a model formulated to see if environmental feedback can free $\Phi$6 from the Prisoner’s dilemma. I’ll also discuss the concept of the Effective Game, which incorporates the frequency and density of different viral types in the environment.

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Random walks on Gromov hyperbolic spaes and Teichmüller spaces. Pacific Dynamics Seminar

Speaker: 
Inhyeok Choi
Date: 
Thu, Jul 22, 2021
Location: 
Online
Zoom
Conference: 
Pacific Dynamics Seminar
Abstract: 

n this talk, I will discuss random walks on Gromov hyperbolic spaces. Due
to the hyperbolicity of the spaces, random walks exhibit behaviors that
differ from the classic (Euclidean) ones. These behaviors include the
escape to infinity, central limit theorems when centered at the escape
rate, and geodesic tracking. I will explain how one can sharpen these
behaviors based on the recent observations by Gouëzel and Baik-Choi-Kim. If
time allows, I will also explain how one can implement this theory on
(non-hyperbolic) Teichmüller spaces.

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Dynamic Self Organization and Microscale Fluid Properties of Nucleoplasm

Speaker: 
Jay Newby
Date: 
Wed, Jul 21, 2021
Location: 
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

The principal function of the nucleus is to facilitate storage, retrieval, and maintenance of the genetic information encoded into DNA and RNA sequences. A unique feature of nucleoplasm—the fluid of the nucleus—is that it contains chromatin (DNA) and RNA.

In contrast to other important biological polymer hydrogels, such as mucus and extracellular matrix, the nucleic acid polymers have a sequence. Recent experiments have shown that during the growth phase of the cell cycle, chromatin condenses in a sequence specific manner into regions within the nucleoplasm, possibly so that functionally related genes are grouped together spatially even though they might be far apart in terms of sequence distance.

At the same time, we are becoming increasingly aware of the role of liquid-liquid phase separation (LLPS) in cellular processes in the nucleus and the cytoplasm. Complex molecular interactions over a wide range of timescales can cause large biopolymers (RNA, protein, etc) to phase separate from the surrounding nucleoplasm into distinct biocondensates (spherical droplets in the simplest cases).

I will discuss recent work modelling the role of nuclear biocondensates in neurodegenerative disease and several ongoing projects related to
modelling and microscopy image analysis.

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Epidemic arrivals and Antibiotic Calenders

Speaker: 
Alastair Jamieson-Lane
Date: 
Wed, Jul 7, 2021
Location: 
Zoom
Online
PIMS, University of British Columbia
Conference: 
Mathematical Biology Seminar
Abstract: 

Here I give two tiny talks on some of my research from the past couple years. In the first half of the talk I re-examine some popular heuristics for epidemic "time of spread" through the world airline network, and use hitting times and branching processes to explore the mathematical underpinnings of these observations. In the second half of the talk, we zoom in to exploring how antibiotics spreads through a single hospital, the various models and their conflicting recommendations. Mostly just some straightforward dynamical systems, with the opportunity for some cute asymptotic arguments on the side.

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Dynamical inference for biological processes through the lens of optimal transport

Speaker: 
Stephen Zhang
Date: 
Wed, Jun 30, 2021
Location: 
Zoom
Online
Conference: 
Mathematical Biology Seminar
Abstract: 

Understanding how cells change their identity and behaviour over time in living systems is a key question in many fields of biology. Measurement of cell states is inherently destructive, and so the relationship of the current state of a cell to some future state, or ‘fate’, cannot be observed experimentally. Trajectory inference refers to the general problem of trying to estimate various aspects of the state-fate relationship. We discuss optimal transport as a useful analytical tool for trajectory inference, and we develop a mathematical framework for recovering trajectories in both non-equilibrium as well as equilibrium systems.

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PIMS EDI Panel: Effective Allyship in STEM

Speaker: 
Sophie MacDonald,
Shirou Wang
Bobby Wilson
Douglas Farenick
Greg Martin
Date: 
Wed, Jun 16, 2021
Location: 
University of British Columbia, Vancouver, Canada
Online
Abstract: 

In recent months, PIMS has been actively engaging in conversations on diversity, equity, and inclusion. Following the Panel on Women in STEM held in May, this next event looks at ways in which effective allyship can build a better and stronger community in the Mathematical Sciences. Being an ally involves much more than passively accepting someone's rights. It is a conscious engagement and active advocacy for those whose voices may be stifled, unheard, or underappreciated. Our panelists look at actionable steps we can take to be better champions in academia.

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Connes fusion of the free fermions on the circle

Speaker: 
Peter Kristel
Date: 
Fri, Jun 11, 2021
Location: 
Zoom
Online
Conference: 
CMS Scientific Session on Quantum Mathematics
Abstract: 

A conformal net on $S^1$ is an assignment $\mathcal{A}:\left\{\textrm{open subsets of } S^1\right\} \to \left\{\mbox{von Neumann algebras acting on } \mathcal{F}\right\}$, which satisfies a slew of axioms motivated by quantum field theory. In this talk, I will consider the free fermionic conformal net. In this case, the Hilbert space $\mathcal{F}$ is the Fock space generated by the positive energy modes of square-integrable spinors on the circle $?^2(?^1,\mathbb{S})$; and the von Neumann algebras are Clifford algebras generated by those elements of $?^2(?^1,\mathbb{S})$ whose support lies in $?\subset ?^1$. After going over this construction, I will argue that given an open interval $?\subset ?^1$, one can equip $\mathcal{F}$ with the structure of $\mathcal{A}(I)-\mathcal{A}(I)$-bimodule. I will then outline the construction of a canonical isomorphism of bimodules $\mathcal{F}\boxtimes_{\mathcal{A}(I_\_)}\mathcal{F}\to\mathcal{F}$ where $\boxtimes_{\mathcal{A}(I_\_)}$ stands for the Connes fusion product over the algebra assigned to the lower semi-circle $I_\_$. If time permits, I will discuss some (anticipated) applications of this isomorphism, for example in string geometry, or in the construction of the free fermion extended topological field theory.

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SU(2) hadrons on a quantum computer

Speaker: 
Jinglei Zhang
Date: 
Fri, Jun 11, 2021
Location: 
Zoom
Online
Conference: 
CMS Scientific Session on Quantum Mathematics
Abstract: 

Lattice gauge theories are relevant in many fields of physics, and simulations with quantum computers can become a powerful tool to study them, especially in regimes inaccessible to classical numerical methods. In particular, non-Abelian gauge theories, which among other things describe fundamental particles’ interactions, are of great interest. In this talk I will discuss the first quantum simulation of a non-Abelian lattice gauge theory that includes dynamical matter. I will show how the theory is formulated in order to include colour degrees of freedom, and how this allows for the existence of baryons in the model, which do not exist in Abelian theories. A quantum computation of the low-lying spectrum of the model is performed on an IBM superconducting platform using a variational quantum eigensolver. This proof-of-concept demonstration was made possible by a resource-efficient approach in the design of the quantum algorithm, and lays out the foundation for further development of the field. This talk is based on arXiv:2102.08920.

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Quantum applications of harmonic analysis on the group of positive rationals

Speaker: 
Artur Sowa
Date: 
Fri, Jun 11, 2021
Location: 
Zoom
Online
Conference: 
CMS Scientific Session on Quantum Mathematics
Abstract: 

Harmonic analysis on the multiplicative group of positive rational numbers (ℚ+) has not been part of the common quantum-theoretic toolkit. In this talk, I will discuss how it lends itself to the analysis of operators in ℓ2(ℕ), in some cases leading to spectacular new insights into their spectral properties. I will also discuss its application in a study of the Bose-Hubbard model, i.e. a model of an array of bosons with the nearest-neighbour interactions. The Fourier transform on ℚ+ uncovers the model's unobvious symmetries and surprising connections with other structures. In addition, I will report a rigorous, albeit computer-assisted, proof of the existence of quantum phase transitions in finite quantum systems of this type. The study of the Bose-Hubbard model has been carried out in collaboration with Prof. Jonas Fransson (Department of Physics and Astronomy, University of Uppsala).

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