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30 Transformation Groups Seminar
Transformation Groups Seminar Speaker: Tao Gong (Western) "Affine toric varieties and cones" Time: 10:30 - 11:30 Room: MC 204 In this lecture, I will give an introduction to toric varieties and cones, and propositions and relations about them. Algebraic Geometry
Algebraic Geometry Speaker: Kumar Shukla (Western) "WAG: Degree and dimension" Time: 15:30 - 15:30 Room: MC 107 |
31 Geometry and Topology
Geometry and Topology Speaker: Sterling Ebel (Western) "Synthetic approach to the Quillen model structure on spaces" Time: 15:30 - 16:30 Room: MC 107 Quillen's construction of a model structure on the category of topological spaces is a fundamental result in homotopy theory. This construction has since been applied to several related categories, such as k-spaces, and the importance of many model categories is justified by their equivalence with Quillen's structure on spaces. In this talk, we will present an axiomatic approach to constructing Quillen's model structure on spaces to apply it to a wider range of settings. As special cases we recover several existing model structures, such as on the categories of sober spaces and of pseudotopological spaces. We also use this approach to construct a novel model structure on the category of locales, making the coreflection to sober spaces a Quillen adjunction. This is joint work with Chris Kapulkin (arXiv:2310.14235). |
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6 Transformation Groups Seminar
Transformation Groups Seminar Speaker: Tao Gong (Western) "Affine toric varieties and cones (Part 2)" Time: 10:30 - 11:30 Room: MC 204 In this lecture, I will give an introduction to toric varieties and cones, and propositions and relations about them.
Algebraic Geometry
Algebraic Geometry Speaker: Nickolas Rieke (Western) "WAG: Affine Varieties" Time: 15:30 - 16:30 Room: MC 107 Pizza Seminar
Pizza Seminar Speaker: Chris Kapulkin (Western) "An invitation to constructive mathematics" Time: 17:00 - 18:00 Room: MC 107 The classical understanding of logic and, by extension, of mathematics
is based upon the notion of truth. In that view, the role of a
mathematical proof is to establish the truth of some statement, at which
point the proof itself can be discarded. For instance, when computing a
derivative, we apply the chain rule, not its proof. Constructive mathematics reverses this approach, focusing primarily on
the notion of a proof itself. It asks that all proofs be effective, thus
rejecting classical principles such as the law of excluded middle.
Initially seen as a largely philosophical position, constructive
mathematics has come back to the forefront, since it is precisely the
kind of mathematics that computers can understand. In this talk, we will explore the main principles of constructive
mathematics as developed by early constructivists: Brouwer and Heyting,
and see how it is used these days by mathematicians around the world who
wish to verify the correctness of their proofs using computers. |
7 Geometry and Topology
Geometry and Topology Speaker: Ajneet Dhillon (Western) "Grothendieck-Lefschetz theorems in algebraic geometry" Time: 15:30 - 16:30 Room: MC 107 This talk is an overview of a genre of theorems called "Grothendieck-Lefschetz theorems". I will start by introducing Lefschetz's original theorem. Our next, stop is Grothendieck's theorem for divisors and line bundles which can be though of as a codimension one Lefschetz theorem in the algebraic category. From this point there are two natural paths to generalisation. The first is to higher codimension subvarieties. In this direction there are some infinitesimal results due to Girivaru-Patel. The second path considers higher rank bundles. The first results in this direction are due to Hartshorne. In joint work with R. Girivaru, Hartshorne's work has been generalised to principal bundles. The talk will end with some applications of our result to splitting criteria.
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9 Graduate Seminar
Graduate Seminar Speaker: Michelle Hatzel (Western) "Continuation Methods for Numerical Problem Solving" Time: 16:30 - 17:30 Room: MC 107 Informally, if two functions can be “continuously deformed†from one to the other, this is called a homotopy. Homotopy emerged from theory more than a century ago and was introduced as a numerical method for solving non-linear problems in the 1960s. The basic components of these early continuation algorithms built on earlier path-tracking methods, which exist in today’s “black box†solvers. We will look at the building blocks of continuation algorithms, how they work (or don’t), and how key insights from the 1970s and 1980s contributed to some powerful polynomial-solving software packages. |
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13 Transformation Groups Seminar
Transformation Groups Seminar Speaker: Larry So (Western) "Toric varieties of fans" Time: 10:30 - 11:30 Room: MC 204 I will define toric varieties associated to fans and give a few examples. Algebraic Geometry
Algebraic Geometry Speaker: Brett Nasserden (Western) "WAG: Projective Varities" Time: 15:30 - 16:30 Room: MC 107 |
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16 Graduate Seminar
Graduate Seminar Speaker: Tao Gong (Western) "What is the space of conjugacy classes?" Time: 16:30 - 17:30 Room: MC 107 When G is a topological group, G acts on itself by conjugation. This leads to the natural question: what is the quotient space of conjugacy classes? In this talk, we will work out the answer to this question in the special case when G is a connected compact simple Lie group – the space is contractible! |
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20 Algebraic Geometry
Algebraic Geometry Speaker: Ajneet Dhillon (Western) "WAG: Low dimensional varieties" Time: 15:30 - 16:30 Room: MC 107 |
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27 Transformation Groups Seminar
Transformation Groups Seminar Speaker: Larry So (Western) "The quotient construction and homogeneous coordinates of toric varieties" Time: 10:30 - 11:30 Room: MC 108 Algebraic Geometry
Algebraic Geometry Speaker: Kate Kim (Western) "WAG: 0-dimensional ideals" Time: 15:30 - 16:30 Room: MC 108 |
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1 Graduate Seminar
Graduate Seminar Speaker: Marwa Tuffaha (Western) "Mutator dynamics cannot be explained by mutation rates alone" Time: 16:30 - 17:30 Room: MC 107 Mutators, cells with elevated mutation rates, are common in both natural microbial populations and in human cancers. Recent experiments have shown that mutators can invade a population, but the invasion dynamics and probability couldn’t be explained by mutation rates alone. Here we show, analytically and in simulation, that mutation bias (which types of mutations are likely to occur) can play an important role in the emergence of mutators. A mutator that reduces or reverses the historically prevailing mutational bias is shown to have an increased chance of invasion, while chances are reduced when the bias is reinforced. These findings are important when trying to understand natural populations or competition experiments with mutators. |
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