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UBC
Mon 24 Feb 2020, 3:00pm
Algebraic Geometry Seminar
MATH 225
Quivers, canonical bases, and categorification
MATH 225
Mon 24 Feb 2020, 3:00pm-4:00pm

#### Abstract

In a famous paper from 2003, Fock and Goncharov conjectured that the algebra of regular functions on a cluster variety has a canonical basis parametrized by the tropicalization of a dual cluster variety. In this talk, I will show how to construct this canonical basis in an interesting class of examples. Using ideas from the representation theory of quivers, I will construct graded vector spaces which categorify the elements of the canonical basis. These graded vector spaces are closely related to spaces of BPS states in supersymmetric quantum field theories.
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University of California, Davis
Tue 25 Feb 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 4133, Library/Seminar Room
Lieb-Robinson bounds for a class of continuum many-body fermion systems
ESB 4133, Library/Seminar Room
Tue 25 Feb 2020, 3:30pm-4:30pm

#### Abstract

We introduce a class of UV-regularized two-body interactions for fermions in \$\R^d\$ and prove a Lieb-Robinson estimate for the dynamics of this class of many-body systems. As a step towards this result, we also prove a propagation bound of Lieb-Robinson type for one-particle Schr\“odinger operators. We apply the propagation bound to prove the existence of a strongly continuous infinite-volume dynamics on the CAR algebra.
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Simon Fraser University
Wed 26 Feb 2020, 1:45pm
Mathematical Biology Seminar
ESB 4133
To oscillate or not? Bacteria regulate partition machinery dynamics to faithfully segregate DNA
ESB 4133
Wed 26 Feb 2020, 1:45pm-2:45pm

#### Abstract

In many bacteria, the segregation of their DNA  is actively transported by a two protein system.  One of the proteins acts as a substrate and binds to DNA in an ATP bound form, while the other stimulates its phosphatase activity, causing it to unbind after  conversion to an ADP bound form.  The result is a burnt-bridges style locomotion where the activity of the proteins generates a spatial gradient of the substrate that can drive motion. When this machinery is segregating low-copy plasmids, experiments show that the plasmids oscillate along the cell length, eventually placing themselves regularly along the cell.  However it is unclear whether these oscillations persist as plasmids continue to replicate, or if system moves to a stable fixed point?  Here I will present a deterministic model for the spatial dynamics of plasmids under the control of this two protein system.  We find that over the course of the cell cycle, through a competition between spatial confinement and fluctuations in the amount of free substrate protein, the system can transition from a stable point to oscillations, then back to a stable point again.  The prediction is that the system measure's cell length via oscillations but eventually gets pushed into a fixed point that faithfully partitions the genetic information.
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UBC
Wed 26 Feb 2020, 3:10pm
Probability Seminar
PIMS lounge
Finitary isomorphisms of continuous-time processes
PIMS lounge
Wed 26 Feb 2020, 3:10pm-4:00pm

#### Abstract

Consider two translation-invariant continuous-time processes X=(X_t) and Y=(Y_t). The two processes are isomorphic if there exists an invertible (bimeasurable) map from X to Y which commutes with translations. The map is finitary if in order to determine a portion of Y one only needs to see a large portion of X. When does such a finitary map exist? We investigate this question, showing, for example, that Brownian motion reflected on an interval is finitarily isomorphic to a Poisson point process (thereby answering a question of Kosloff and Soo).
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University of Victoria
Wed 26 Feb 2020, 3:15pm
Topology and related seminars
ESB 4127
Isotopy in dimension 4
ESB 4127
Wed 26 Feb 2020, 3:15pm-10:00am

#### Abstract

I will describe why the trivial knot S2-->S4 has non-unique spanning discs up to isotopy. This comes from a chain of deductions that include a description of the low-dimensional homotopy-groups of embeddings of S1 in S1xSn (for n>2), a group structure on the isotopy-classes of reducing discs of S1xDn, and the action of the diffeomorphism group Diff(S1xSn) on the embedding space Emb(S1, S1xSn).  Roughly speaking, these results say there is no direct translation from dimension 3 to 4, for the Hatcher-Ivanov theorems on spaces of incompressible surfaces. Or said another way, isotopy in dimension 4 is more closely analogous to isotopy in high dimensions.
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The American University of Paris
Thu 27 Feb 2020, 3:30pm SPECIAL
Number Theory Seminar
Math 126
On the distribution of Hecke eigenvalues in the complex plane.
Math 126
Thu 27 Feb 2020, 3:30pm-4:30pm

#### Abstract

Let r be a cuspidal automorphic representation of
non-solvable polyhedral type for GL(2) over a number field. We

establish the existence of sets of primes with positive upper

Dirichlet density for which the associated Hecke eigenvalues satisfy

prescribed bounds on their argument and/or size. For example, if r is

not self-dual we show that there is a positive upper density of Hecke

eigenvalues in any sector of size 2.64 radians.

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UCLA
Fri 28 Feb 2020, 3:00pm
Department Colloquium
ESB 2012
PIMS distinguished visitor colloquium: Dynamics of Congested Crowds and incompressible fluids
ESB 2012
Fri 28 Feb 2020, 3:00pm-3:50pm

#### Abstract

In this talk we will first discuss Crowd motions in emergency evacuation setting. Then we will discuss its relevance to the transport of incompressible fluids. We formulate these motions as ``gradient flows", i.e. an evolution that moves to dissipate their free energy as fast as possible. The gradient flow structure allows variational methods to study time-dependent problems. Our goal is to establish global-time existence of solutions past potential topological or geometrical singularities. We will survey relevant results in the literature, open problems, and then report a recent result.
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École Polytechnique
Mon 2 Mar 2020, 3:00pm
Algebraic Geometry Seminar
MATH 225
TBA
MATH 225
Mon 2 Mar 2020, 3:00pm-4:00pm

#### Abstract

TBA
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UCLA
Tue 3 Mar 2020, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar / PIMS Seminars and PDF Colloquiums
PIMS lounge
PIMS distinguished visitor minicourse: Gradient flows and minimizing movements. Lecture 1
PIMS lounge
Tue 3 Mar 2020, 3:30pm-4:30pm

#### Abstract

We will discuss Gradient flow structures in parabolic type PDEs and interface motions. Such structure introduces physical interpretations to time-dependent PDEs in terms of energy dissipation, and allows a weak notion of global-time solutions to nonlinear PDE problems. In broader terms, we will discuss minimizing movements, which approximates dissipative PDE systems with a discrete-time optimization problem. Lecture 1 will be a general introduction. Lecture 2 and 3 will discuss specific examples of minimizing movements: the mean curvature flow and nonlinear diffusions with Darcy's law.

#### Note for Attendees

The first lecture in the series of 3 lectures.
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University of British Columbia
Wed 4 Mar 2020, 1:45pm
Mathematical Biology Seminar
ESB 4133
Random approaches to decipher DNA-encoded gene regulatory logic
ESB 4133
Wed 4 Mar 2020, 1:45pm-2:45pm

#### Abstract

The many different cell types and states result in large part from the different sets of genes they express. Gene expression level is encoded in the DNA sequence of the genome, and is interpreted by sequence-specific proteins called "transcription factors" (TFs). While characteristics of how TFs work are known, we lack a quantitative understanding of their function. Here, I describe a strategy using random DNA for building such a quantitative understanding, using yeast as a model system. I will provide a basic overview of how TFs recognize DNA, and why random DNA provides ideal gene regulatory "big data" for learning the relationship between DNA sequence and expression level. Using this strategy, we train highly complex models that learned a great deal about the biochemistry of transcriptional regulation, and gain insight into the activities of regulatory mutations.
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UBC
Wed 4 Mar 2020, 3:15pm
Probability Seminar
PIMS lounge
Random Cayley graphs
PIMS lounge
Wed 4 Mar 2020, 3:15pm-4:05pm

#### Abstract

We consider the random Cayley graph of a finite group G formed by picking k random generators uniformly at random:
(1) We prove universality of cutoff (for the random walk) and a concentration of measure phenomenon in the Abelian setup (namely, that all but $o(|G|)$ elements lie at distance [R-o(R),R+o(R)] from the origin, where R is the minimal ball in Z^k of size at least |G|), provided k-d(G) >> 1 where d(G) is the size of the smallest generating set of G. As conjectured by Aldous and Diaconis, the cutoff time is typically independent of the algebraic structure (it is given by the time at which the entropy of a random walk on Z^k is log |G|).
(2) We prove analogous results for the Heisenberg groups  of  d x d uni-upper triangular matrices with entries defined mod p, for p prime.
(3) Lastly, we resolve a conjecture of D. Wilson that if G is a group of size at most 2^d then for all k the mixing time of random walk on a Cayley graph of G with k random generators is as rapid as that of Z_2^d and likewise.
(Joint work with Sam Thomas.)
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UCLA
Thu 5 Mar 2020, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar / PIMS Seminars and PDF Colloquiums
PIMS lounge
PIMS distinguished visitor minicourse: Gradient flows and minimizing movements. Lecture 2.
PIMS lounge
Thu 5 Mar 2020, 3:30pm-4:30pm

#### Abstract

We will discuss Gradient flow structures in parabolic type PDEs and interface motions. Such structure introduces physical interpretations to time-dependent PDEs in terms of energy dissipation, and allows a weak notion of global-time solutions to nonlinear PDE problems. In broader terms, we will discuss minimizing movements, which approximates dissipative PDE systems with a discrete-time optimization problem. Lecture 1 will be a general introduction. Lecture 2 and 3 will discuss specific examples of minimizing movements: the mean curvature flow and nonlinear diffusions with Darcy's law.

#### Note for Attendees

The second lecture in the series of 3 lectures.
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Rebeca Cardim Falcao
UBC MATH
Fri 6 Mar 2020, 3:00pm
Department Colloquium
ESB 2012
ESB 2012
Fri 6 Mar 2020, 3:00pm-3:50pm

#### Abstract

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UBC
Mon 9 Mar 2020, 3:00pm
Algebraic Geometry Seminar
MATH 225
TBA
MATH 225
Mon 9 Mar 2020, 3:00pm-4:00pm

#### Abstract

TBA
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Frederic Gibou
U. of California, Santa Barbara
Mon 9 Mar 2020, 3:00pm
Institute of Applied Mathematics
LSK 460
IAM-PIMS Distinguished Colloquium: On the Edge: Sharp Treatment of Free Boundary Problems and Applications
LSK 460
Mon 9 Mar 2020, 3:00pm-4:00pm

#### Abstract

Most modern problems in science and engineering are described on irregular geometries or free boundaries that are notoriously difficult to handle numerically. In addition, the differences in length scale and the limitation of computational resources necessitate the use of adaptive grids for their numerical approximations. I will discuss a numerical strategies based on the level-set method, sharp treatment of boundary conditions and Quad/Oc-tree cartesian grids on massively parallel architecture. I will also consider some applications from materials, fluid dynamics and biology.

Bio:

Professor Gibou is a faculty member in the Department of Mechanical Engineering, in the Department of Computer Science and in the Department of Mathematics at the University of California, Santa Barbara. He currently is the Chair of the Department of Mechanical Engineering. He received his PhD from the Applied Mathematics Department at UCLA, working with Stan Osher and Russ Caflisch, and did his post-doctoral research in the Departments of Mathematics and Computer Science at Stanford University working with Ron Fedkiw. He was awarded an Alfred P. Sloan Fellowship in Mathematics, the Regent’s Junior Faculty Fellowship, and the Robert Sorgenfrey Distinguished Teaching award. Professor Gibou is on the Editorial Board of the Journal of Computational Physics. His research is at the interface between Applied Mathematics, Computer Science and Engineering Sciences. It is focused on the design of a novel paradigm for high resolution computational methods for large scale computations and their use for a variety of applications including Computational Materials Science, Computational Fluid Dynamics and Computational Biology.

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UCLA
Tue 10 Mar 2020, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar / PIMS Seminars and PDF Colloquiums
PIMS lounge
PIMS distinguished visitor minicourse: Gradient flows and minimizing movements. Lecture 3.
PIMS lounge
Tue 10 Mar 2020, 3:30pm-4:30pm

#### Abstract

We will discuss Gradient flow structures in parabolic type PDEs and interface motions. Such structure introduces physical interpretations to time-dependent PDEs in terms of energy dissipation, and allows a weak notion of global-time solutions to nonlinear PDE problems. In broader terms, we will discuss minimizing movements, which approximates dissipative PDE systems with a discrete-time optimization problem. Lecture 1 will be a general introduction. Lecture 2 and 3 will discuss specific examples of minimizing movements: the mean curvature flow and nonlinear diffusions with Darcy's law.

#### Note for Attendees

The third lecture in the series of 3 lectures.
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Ohio State University
Tue 10 Mar 2020, 4:00pm
Discrete Math Seminar
ESB 4127
TBA
ESB 4127
Tue 10 Mar 2020, 4:00pm-10:00am

#### Abstract

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Duke
Wed 11 Mar 2020, 3:15pm
Probability Seminar
ESB 4133, PIMS Library/Seminar Room
TBA
ESB 4133, PIMS Library/Seminar Room
Wed 11 Mar 2020, 3:15pm-4:15pm

#### Abstract

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Penn State University
Thu 12 Mar 2020, 3:30pm
Number Theory Seminar
MATH 126
TBA
MATH 126
Thu 12 Mar 2020, 3:30pm-5:00pm

#### Abstract

TBA
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Pennsylvania State University
Fri 13 Mar 2020, 3:00pm
Department Colloquium
ESB 2012
Faculty of Science Early Career Colloquium series: TBA
ESB 2012
Fri 13 Mar 2020, 3:00pm-3:50pm

#### Abstract

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UMass Amherst
Mon 16 Mar 2020, 3:00pm
Algebraic Geometry Seminar
MATH 225
New rational cubic fourfolds arising from Cremona transformations
MATH 225
Mon 16 Mar 2020, 3:00pm-4:00pm

#### Abstract

It is conjectured that two cubic fourfolds are birational if their associated K3 categories are equivalent. We prove this conjecture for very general cubic fourfolds containing a Veronese surface, where the birational maps are induced from a Cremona transformation. Using these birational maps, we find new rational cubic fourfolds. This is joint work with Yu-Wei Fan.
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Kanazawa University, Japan
Tue 17 Mar 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 4133, Library/Seminar Room
Viscosity approach to the crystalline mean curvature flow
ESB 4133, Library/Seminar Room
Tue 17 Mar 2020, 3:30pm-4:30pm

#### Abstract

In this talk I will give an overview of the notion of viscosity solutions for the crystalline mean curvature flow in an arbitrary dimension, introduced recently in joint work with Yoshikazu Giga from the University of Tokyo. This problem serves as a model of crystal growth but it also has applications in image processing and related fields. Its level set formulation leads to a nonlocal, very singular parabolic equation with non-smooth, faceted solutions to which the standard viscosity theory does not apply. We introduce a reduced class of faceted test functions and show that they are sufficient to establish the comparison principle as well as an existence result for a rather general class of problems with the crystalline mean curvature.
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Chris Liaw
Wed 18 Mar 2020, 3:15pm
Probability Seminar
ESB 4133, PIMS Library/Seminar Room
TBA
ESB 4133, PIMS Library/Seminar Room
Wed 18 Mar 2020, 3:15pm-4:05pm

#### Abstract

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UBC MATH
Fri 20 Mar 2020, 3:00pm
Department Colloquium
ESB 2012
ESB 2012
Fri 20 Mar 2020, 3:00pm-3:50pm

#### Abstract

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University of Victoria
Tue 24 Mar 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 4133, Library/Seminar Room
Snaking Bifurcations in Higher Space Dimensions
ESB 4133, Library/Seminar Room
Tue 24 Mar 2020, 3:30pm-4:30pm

#### Abstract

In this talk we will discuss how bistability in a spatially extended system can lead to fascinating localized steady-state solutions. We will primarily focus on the Swift-Hohenberg equation, which is a is known to support a variety of spatially localized steady-states. In one spatial dimensional the Swift-Hohenberg equation exhibits spatially localized steady-state solutions which give way to a bifurcation structure known as snaking. That is, these solutions bounce between two different values of the bifurcation parameter while ascending in norm. The mechanism that drives snaking in one spatial dimension is now well-understood, but recent numerical investigations indicate that upon moving to two spatial dimensions, radially-symmetric and hexagonal spatially-localized solutions take on a significantly different snaking structure. This talk details my recent work on explaining the bifurcation structure of localized solutions in higher space dimensions as well as discussing a number of open problems related to the formation of localized structures in bistable systems.
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Zhen-Qing Chen
Wed 25 Mar 2020, 3:15pm
Probability Seminar
ESB 4133, PIMS Library/Seminar Room
TBA
ESB 4133, PIMS Library/Seminar Room
Wed 25 Mar 2020, 3:15pm-4:05pm

#### Abstract

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UBC MATH
Fri 27 Mar 2020, 3:00pm
Department Colloquium
ESB 2012
ESB 2012
Fri 27 Mar 2020, 3:00pm-3:50pm

#### Abstract

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U. of Sussex
Mon 30 Mar 2020, 3:00pm
Institute of Applied Mathematics
LSK 460
IAM Distinguished Alumni Lecture: A Robust and Efficient Adaptive Multigrid Solver for Geometric Evolution Laws with Applications to Cell Migration
LSK 460
Mon 30 Mar 2020, 3:00pm-4:00pm

#### Abstract

In this talk, I will present a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution laws. The optimal control of geometric evolution laws arises in a number of applications in fields including material science, image processing, tumour growth and cell motility.

Despite this, many open problems remain in the analysis and approximation of such problems. In the current work we focus on a phase field formulation of the optimal control problem, hence exploiting the well developed mathematical theory for the optimal control of semilinear parabolic partial differential equations. Approximation of the resulting optimal control problem is computationally challenging, requiring massive amounts of computational time and memory storage.

The main focus of this work is to propose, derive, implement and test an efficient solution method for such problems. The solver for the discretised partial differential equations is based upon a geometric multigrid method incorporating advanced techniques to deal with the nonlinearities in the problem and utilising adaptive mesh refinement. An in-house two-grid solution strategy for the forward and adjoint problems, that significantly reduces memory requirements and CPU time, is proposed and investigated computationally. Furthermore, parallelisation as well as an adaptive-step gradient update or the control are employed to further improve efficiency. Along with a detailed description of our proposed solution method together with its implementation we present a number of computational results that demonstrate and evaluate our algorithms with respect to accuracy and
efficiency.

A highlight of the present work is simulation results on the optimal control of phase field formulations of geometric evolution laws in 3-D which would be computationally infeasible without the solution strategies proposed in the present work.

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Slim Ibrahim
University of Victoria
Tue 31 Mar 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 4133, Library/Seminar Room
TBA
ESB 4133, Library/Seminar Room
Tue 31 Mar 2020, 3:30pm-4:30pm

#### Abstract

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Chen Wang
UBC MATH
Fri 3 Apr 2020, 3:00pm
Department Colloquium
ESB 2012
ESB 2012
Fri 3 Apr 2020, 3:00pm-3:50pm

#### Abstract

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Peter Sternberg
University of Indiana-Bloomington
Tue 7 Apr 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS Lounge
TBA
PIMS Lounge
Tue 7 Apr 2020, 3:30pm-4:30pm

#### Abstract

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UBC
Wed 8 Apr 2020, 3:15pm
Probability Seminar
PIMS lounge
TBA
PIMS lounge
Wed 8 Apr 2020, 3:15pm-4:00pm

#### Abstract

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Max-Planck Institute for Evolutionary Biology
Wed 29 Apr 2020, 2:45pm
Mathematical Biology Seminar
ESB 4133
TBA
ESB 4133
Wed 29 Apr 2020, 2:45pm-3:45pm

#### Abstract

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Max-Planck Institute for Evolutionary Biology
Fri 1 May 2020, 3:00pm
Department Colloquium
ESB 2012
(PIMS/UBC distinguished colloquium) TBA
ESB 2012
Fri 1 May 2020, 3:00pm-4:00pm

#### Abstract

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Northwestern University
Fri 25 Sep 2020, 2:45pm
Mathematical Biology Seminar
ESB 4133
TBA
ESB 4133
Fri 25 Sep 2020, 2:45pm-3:45pm

TBA

#### Note for Attendees

Prof Volkening will also deliver the Rising Stars colloquium on Nov 6, 2020.
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Northwestern University
Fri 6 Nov 2020, 3:00pm SPECIAL
Department Colloquium
ESB 1012
TBA
ESB 1012
Fri 6 Nov 2020, 3:00pm-4:00pm

TBA

#### Note for Attendees

Rising Stars Colloquium
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ETH Zurich, will move to NYU
Fri 20 Nov 2020, 3:00pm
Department Colloquium
TBD
Faculty of Science Early Career Invited Lecture: TBD
TBD
Fri 20 Nov 2020, 3:00pm-3:50pm

#### Abstract

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UC Irvine
Thu 18 Mar 2021, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
TBA
TBA
TBA
Thu 18 Mar 2021, 3:30pm-4:30pm

#### Abstract

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UC Irvine
Fri 19 Mar 2021, 3:00pm
Department Colloquium
TBA
PIMS-UBC Rising Star Colloquium
TBA
Fri 19 Mar 2021, 3:00pm-4:00pm

#### Abstract

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Conor Mooney
Fri 19 Mar 2021, 3:00pm SPECIAL
Rising Star Colloquium
Fri 19 Mar 2021, 3:00pm-4:00pm

#### Details

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Ciprian Manolescu
Stanford University
Fri 9 Apr 2021, 3:00pm
Department Colloquium
ESB1012
PIMS-UBC Distinguished Colloquium
ESB1012
Fri 9 Apr 2021, 3:00pm-4:00pm

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