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 Events
University of Colorado
Mon 18 Mar 2019, 4:00pm
Algebraic Geometry Seminar
MATH 126
Distinguished models of intermediate Jacobians
MATH 126
Mon 18 Mar 2019, 4:00pm-5:00pm

Abstract

In this talk I will discuss joint work with J. Achter and C. Vial showing that the image of the Abel--Jacobi map on algebraically trivial cycles descends to the field of definition for smooth projective varieties defined over subfields of the complex numbers.  The main focus will be on applications to topics such as: descending cohomology geometrically, a conjecture of Orlov regarding the derived category and Hodge theory, and motivated admissible normal functions.
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Sandy Irani
University of California at Irvine
Mon 18 Mar 2019, 4:00pm
Institute of Applied Mathematics
ESB 4133
Computational Complexity of Quantum Systems
ESB 4133
Mon 18 Mar 2019, 4:00pm-5:00pm

Abstract

One of the goals of quantum information theory is to understand quantum systems from the standpoint of computational complexity. How difficult is it to compute fundamental properties of a quantum system or simulate a particular system over time? Physicists have been using computers for decades to understand various aspects of quantum systems, but these methods are typically heuristic and achieve success on only limited classes of systems. This talk will give an overview of recent developments in the effort to understand these problems from a formal complexity-theoretic point of view. In particular, one of the most basic properties of a system is its lowest energy state or ground state. I will survey results on the complexity of ground states and the computational resources required to compute them. I will also discuss heuristics to find ground states on more near-term quantum computers.

 

Note for Attendees

Please join the reception immediately preceding the talk (same venue), 3:30-4:00. Send email to Anna Eberhard <anna.eberhard@ubc.ca> if you would like to meet with Professor Irani on that Monday.
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Edmond Chow
Sch of Computational Science & Engineering, Georgia Institute of Technology
Tue 19 Mar 2019, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS lounge)
Asynchronous Iterative Methods
ESB 4133 (PIMS lounge)
Tue 19 Mar 2019, 12:30pm-1:30pm

Abstract

The standard iterative methods for solving linear and nonlinear systems of equations are all synchronous, meaning that in the parallel execution of these methods where some processors may complete an iteration before other processors (for example, due to load imbalance), the fastest processors must wait for the slowest processors before continuing to the next iteration.  This talk will discuss parallel iterative methods that operate asynchronously, meaning that the processors never wait for each other, but instead proceed using whatever iterate values are already available from other processors.  Processor idle time is thus eliminated, but questions arise about the convergence of these methods.  Asynchronous iterative methods will be introduced using simple fixed-point iterative methods for linear systems, before discussing asynchronous versions of rapidly converging methods, in particular, optimized Schwarz and multigrid methods.

Note for Attendees

A light lunch (sushi) will be served.
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Johns Hopkins University
Tue 19 Mar 2019, 4:00pm
Institute of Applied Mathematics
ESB 4133
Sublinearity in Integer Optimization
ESB 4133
Tue 19 Mar 2019, 4:00pm-5:00pm

Abstract

Cutting plane techniques are key to solving large scale optimization problems with mixed-integer variables. Modern approaches to cutting plane theory shows that the concept of sublinearity is a unifying way to organize these ideas. This leads to a rich interplay of ideas between convex analysis and geometry, geometry of numbers and functional analysis. We will survey this modern viewpoint of cutting plane theory. No background in mixed-integer optimization or convex analysis will be assumed.

Note for Attendees

Please join the reception immediately preceding the talk (same venue), 3:30-4:00.
Send email to Anna Eberhard <anna.eberhard@ubc.ca> if you would like to meet with Professor Basu during his visit to UBC, Tuesday to Thursday.
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UBC
Wed 20 Mar 2019, 3:00pm
Probability Seminar
ESB 1012
On the range of lattice models in high dimensions
ESB 1012
Wed 20 Mar 2019, 3:00pm-4:00pm

Abstract

We investigate the scaling limit of the range (the set of visited vertices) for a general class of critical lattice models, starting from a single initial particle at the origin.  Conditions are given on the random sets and an associated ``ancestral relation" under which, conditional on long-term survival, the rescaled ranges converge weakly to the range of super-Brownian motion as random sets. These hypotheses also give precise asymptotics for the limiting behaviour of the probability of exiting a large ball. Applications include voter models, contact processes, oriented percolation and lattice trees.  This is joint work with Mark Holmes and also features work of Akira Sakai and Gord Slade.
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Johns Hopkins University
Thu 21 Mar 2019, 12:30pm
Institute of Applied Mathematics
ESB 4133
Minimal Sublinear Representations of Convex Sets
ESB 4133
Thu 21 Mar 2019, 12:30pm-1:30pm

Abstract

It is well-known that a closed convex set C containing the origin in its interior can be represented as the 1-sublevel set of its gauge function. If the set C is compact, then the gauge is the unique sublinear function whose 1-sublevel coincides with C. However, if C is not compact, there can be multiple different sublinear functions whose 1-sublevels coincide with C. We call any such function a sublinear representation of C. It is not hard to see that the gauge of C is the largest sublinear representation of C, with respect to pointwise dominance. We show that there is a unique smallest sublinear representation f^ of C, i.e., f <= f for any other sublinear representation f of C. The gauge, which is the largest sublinear representation of C, is well-known to be equal to the support function of the polar of C. We associate the notion of a “prepolar” with other sublinear representations and show that the geometric analog of the smallest sublinear representation is the concept of the smallest “prepolar”, with respect to set inclusion. This smallest “prepolar” has an explicit description, just like the classical polar.


Note for Attendees

Sushi served for lunch.
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UBC Mathematics
Fri 22 Mar 2019, 3:00pm
Department Colloquium
ESB 2012
Graduate Research Award: Essential dimension of representations of algebras
ESB 2012
Fri 22 Mar 2019, 3:00pm-4:00pm

Abstract

Let A be a finite-dimensional algebra. A fundamental theorem of Drozd shows that the complexity of the representation theory of A belongs to exactly one of three rather distinct classes, called finite, tame or wild representation type. I will explain how the notion of essential dimension determines the representation type of A. I will go further and define new numerical invariants of A that refine the representation type of A. I will then determine these invariants explicitly in the special case of quiver algebras.

Note for Attendees

Refreshments will be served at 2:30 p.m. in ESB 4133 (Lounge).
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