www.mathtube.org - Mathematics
http://www.mathtube.org/taxonomy/term/103/0
enSurjectivity of random integral matrices on integral vectors
http://www.mathtube.org/lecture/video/surjectivity-random-integral-matrices-integral-vectors
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Speaker: </div>
Melanie Matchett Wood </div>
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Date: </div>
<span class="date-display-single">Fri, Nov 8, 2019</span> </div>
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Location: </div>
PIMS, University of British Columbia </div>
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Conference: </div>
PIMS Distinguished Colloquium </div>
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A random nxm matrix gives a random linear transformation from \Z^m to \Z^n (between vectors with integral coordinates). Asking for the probability that such a map is injective is a question of the non-vanishing of determinants. In this talk, we discuss the probability that such a map is surjective, which is a more subtle integral question. We show that when m=n+u, for u at least 1, as n goes to infinity, the surjectivity probability is a non-zero product of inverse values of the Riemann zeta function. This probability is universal, i.e. we prove that it does not depend on the distribution from which you choose independent entries of the matrix, and this probability also arises in the Cohen-Lenstra heuristics predicting the distribution of class groups of real quadratic fields. This talk is on joint work with Hoi Nguyen. </div>
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ScientificMathematicsProbabilityFri, 06 Dec 2019 18:17:22 +0000root751 at http://www.mathtube.orgScalable approximation of integrals using non-reversible methods: from Riemann to Lebesgue, and why you should care
http://www.mathtube.org/lecture/video/scalable-approximation-integrals-using-non-reversible-methods-riemann-lebesgue-and-why
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Speaker: </div>
Alexandre Bouchard Côté </div>
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Date: </div>
<span class="date-display-single">Fri, Nov 15, 2019</span> </div>
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Location: </div>
PIMS, University of British Columbia </div>
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Conference: </div>
PIMS - UBC Mathematical Sciences Young Faculty Award </div>
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<p>How to approximate intractable integrals? This is an old problem which is still a pain point in many disciplines (including mine, Bayesian inference, but also statistical mechanics, computational chemistry, combinatorics, etc).</p>
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<p>The vast majority of current work on this problem (HMC, SGLD, variational) is based on mimicking the field of optimization, in particular gradient based methods, and as a consequence focusses on Riemann integrals. This severely limits the applicability of these methods, making them inadequate to the wide range of problems requiring the full expressivity of Lebesgue integrals, for example integrals over phylogenetic tree spaces or other mixed combinatorial-continuous problems arising in networks models, record linkage and feature allocation.</p>
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<p>I will describe novel perspectives on the problem of approximating Lebesgue integrals, coming from the nascent field of non-reversible Monte Carlo methods. In particular, I will present an adaptive, non-reversible Parallel Tempering (PT) allowing MCMC exploration of challenging problems such as single cell phylogenetic trees.</p>
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<p>By analyzing the behaviour of PT algorithms using a novel asymptotic regime, a sharp divide emerges in the behaviour and performance of reversible versus non-reversible PT schemes: the performance of the former eventually collapses as the number of parallel cores used increases whereas non-reversible benefits from arbitrarily many available parallel cores. These theoretical results are exploited to develop an adaptive scheme approximating the optimal annealing schedule.</p>
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<p>My group is also interested in making these advanced non-reversible Monte Carlo methods easily available to data scientists. To do so, we have designed a Bayesian modelling language to perform inference over arbitrary data types using non-reversible, highly parallel algorithms.</p> </div>
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ScientificMathematicsStatisticsWed, 04 Dec 2019 20:20:58 +0000root750 at http://www.mathtube.orgIf Space Turned out to be Time: Resonances and Patterns in the Visual Cortex
http://www.mathtube.org/lecture/video/if-space-turned-out-be-time-resonances-and-patterns-visual-cortex
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Speaker: </div>
Bard Ermentrout </div>
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Date: </div>
<span class="date-display-single">Wed, Oct 9, 2019</span> </div>
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Location: </div>
PIMS, University of Manitoba </div>
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Conference: </div>
PIMS-UManitoba Distinguished Lecture </div>
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<p>When subjects are exposed to full field flicker in certain frequencies, they perceive a variety of complex geometric patterns that are often called flicker hallucinations. On the other had, when looking at high contrast geometric patterns like op art, shimmering and flickering is observed. In some people, flicker or such op art can induce seizures. In this talk, I describe a simple network model of excitatory and inhibitory neurons that comprise the visual area of the brain. I show that these phenomena are reproduced and then give an explanation based on symmetry breaking bifurcations and Floquet theory. Symmetric bifurcation theory also shows why one expects a different class of patterns at high frequencies from those at low frequencies.</p>
<p>On the other hand, the visual system is also very sensitive to specific spatial frequencies and this sensitivity can be pathological in the case of so-called pattern-senstive epilepsy. It has been shown that certain types of "op art"can cause visual discomfort. We show that the network that we used in flicker is also sensitive to spatially periodic inputs and suggest that a Hopf bifurcation instability is responsible for the discomfort and seizures.</p>
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<h4>Speaker Biography</h4>
<p>Bard Ermentrout received his PhD in Theoretical Biology at the University of Chicago and was a postdoctoral fellow at the NIH from 1979-1982. He has been at the University of Pittsburgh since then. He is the author of over 200 papers and two books as well as the simulation package, XPPAUT. He is a Sloan Fellow and a SIAM Fellow and received the Mathematical Neuroscience Prize in 2015.</p> </div>
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ScientificMathematical BiologyMathematicsFri, 08 Nov 2019 23:32:05 +0000root749 at http://www.mathtube.orgAn Application of Homotopy Theory to Condensed Matter Physics
http://www.mathtube.org/lecture/video/application-homotopy-theory-condensed-matter-physics
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Speaker: </div>
Daniel Freed </div>
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Date: </div>
<span class="date-display-single">Mon, Sep 16, 2019</span> </div>
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Location: </div>
PIMS, University of Saskatchewan </div>
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Conference: </div>
Peter Scherk Lecture in Geometry </div>
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The classification of phases of matter is a topic of much current interest. While descriptions of quantum mechanical systems often use discrete lattice models, one can typically approximate by continuous field theories. There is a well-developed mathematical framework for studying field theories, and this brings powerful techniques to the table. In this general talk, I will describe joint work with Mike Hopkins (Harvard) in which we carry out this scheme for invertible phases of matter and deduce the classification in terms of bordism groups of manifolds. Much of the talk will focus on general ideas at an elementary level. </div>
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ScientificMathematicsFri, 11 Oct 2019 23:51:36 +0000root748 at http://www.mathtube.orgDINOSAUR WARS: Extinction by Asteroid or Volcanism? Are we the Dinosaurs of the 6th Mass Extinction?
http://www.mathtube.org/lecture/video/dinosaur-wars-extinction-asteroid-or-volcanism-are-we-dinosaurs-6th-mass-extinction
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Speaker: </div>
Gerta Keller </div>
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Date: </div>
<span class="date-display-single">Wed, Jul 24, 2019</span> </div>
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Location: </div>
PIMS, University of Victoria </div>
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Conference: </div>
Hugh C. Morris Lecture </div>
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<p>For the past 40 years the demise of the dinosaurs has been attributed to an asteroid impact on Yucatan, a theory that is imaginative, popular and even sexy. From the very beginning, scientists who doubted this theory were threatened into silence or their careers destroyed by the main theory proponents. Thus began the Dinosaur wars in 1980 – and still continuing. As in any war, there are two sides to the Dinosaur wars. The majority believes an asteroid hit Yucatan and instantaneously wiped out 75% of all life including the dinosaurs in a global firestorm and nuclear type winter. A small minority tested this theory and found contrary evidence that supported Deccan volcanism in India that caused rapid climate warming due to greenhouse gases (CO2), environmental stress, acid rain and ocean acidification culminating in the mass extinctions. This lecture highlights the four decades of the dinosaur wars, the increasing acceptance of volcanism’s catastrophic effects and likely cause of the mass extinction and the resulting ad hoc revisions to accommodate the impact theory. The talk ends with the ongoing 6th mass extinction initiated by rapid fuel burning that is causing the most rapid climate warming in Earth’s history and ocean acidification, which is predicted to reach the 6th mass extinction in as little as 50-75 years and maximum of 250 years. We could be the Dinosaurs of the 6th mass extinction.</p>
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<h3>Speaker Biography</h3>
<p>Gerta Keller is Professor of Paleontology and Geology in the Geosciences Department of Princeton University since 1984. She was born on March 7, 1945 in Liechtenstein. She grew up on a small farm in Switzerland as the sixth of a dozen children with no prospect for education. At age 14 she entered apprenticeship as dressmaker, at 17 she worked for the DIOR Fashion House in Zurich. With no prospect for advancement she began her adventure travels through North Africa and the Middle East, supporting herself by waitressing. She immigrated to Australia at 21, was shot by a bank robber and nearly died at 22. After recovery, she resumed her adventure travels through Southeast Asia and arrived in San Francisco in 1968. There she found the first opportunity for education and entered City College, continued her undergraduate studies at San Francisco State College majoring in Anthropology and Geology, concentrating on climate and environmental changes and their effects on mass extinctions. She was awarded a Danforth Fellowship for her graduate studies at Stanford University in 1974 and received her PhD in 1978. She continued her work at Stanford University and the U.S. Geological Survey in Menlo Park and steadily researched climatic and environmental effects on life all the way back to the dinosaur mass extinction 66 million years ago. In 1984 she was hired as tenured faculty at Princeton University.</p>
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<p>Prof. Gerta Keller’s major research and discoveries ranged from climate change and its effects on ocean circulation, ocean anoxic events, polar warming, Deccan volcanism, comet showers, extraterrestrial impacts, the dinosaur mass extinction, the age of the Chicxulub impact and the 6th mass extinction. Her research frequently challenged accepted scientific dogma and placed her at the center of acrimonious debates fighting for survival of truth-based evidence. All but the cause of the Chicxulub impact were soon accepted by scientists and integrated into new research. After four decades, impact proponents still fiercely defend the impact theory, deny contrary evidence and at best incorporate volcanism as ad hoc revisions, proclaiming the impact triggered volcanism that caused the mass extinction.</p>
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<p>Gerta Keller has over 260 scientific publications in international journals and is a leading authority on catastrophes and mass extinctions, and the biotic and environmental effects of impacts and volcanism. She has co-authored and edited several books and she has been featured in many films and documentaries by very popular TV channels and Film Corporations, including BBC, The History Channel, and Hollywood.</p> </div>
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ScientificMathematical BiologyMathematicsTue, 30 Jul 2019 19:24:05 +0000root747 at http://www.mathtube.orgGeometricity and Galois actions on fundamental groups
http://www.mathtube.org/lecture/video/geometricity-and-galois-actions-fundamental-groups
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Daniel Litt </div>
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Date: </div>
<span class="date-display-single">Fri, Jun 14, 2019</span> </div>
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Location: </div>
PIMS, University of British Columbia </div>
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Conference: </div>
Workshop on Arithmetic Topology </div>
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Which local systems on a Riemann surface X arise from geometry, i.e. as (subquotients of) monodromy representations on the cohomology of a family of varieties over X? For example, what are the possible level structures on Abelian schemes over X? We describe several new results on this topic which arise from an analysis of the outer Galois action on etale fundamental groups of varieties over finitely generated fields. </div>
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ScientificMathematicsTopologySat, 29 Jun 2019 00:42:33 +0000root743 at http://www.mathtube.orgThe stable cohomology of the moduli space of curves with level structures
http://www.mathtube.org/lecture/video/stable-cohomology-moduli-space-curves-level-structures
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Speaker: </div>
Andrew Putman </div>
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<span class="date-display-single">Fri, Jun 14, 2019</span> </div>
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PIMS, University of British Columbia </div>
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Workshop on Arithmetic Topology </div>
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I will prove that in a stable range, the rational cohomology of the moduli space of curve with level structures is the same as the ordinary moduli space of curves: a polynomial ring in the Miller-Morita-Mumford classes. </div>
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ScientificMathematicsTopologySat, 29 Jun 2019 00:25:47 +0000root742 at http://www.mathtube.orgConjectures, heuristics, and theorems in arithmetic statistics - 2 of 2
http://www.mathtube.org/lecture/video/conjectures-heuristics-and-theorems-arithmetic-statistics-2-2
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Speaker: </div>
Wei Ho </div>
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PIMS, University of British Columbia </div>
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Conference: </div>
Workshop on Arithmetic Topology </div>
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We will begin by surveying some conjectures and heuristics in arithmetic statistics, most relating to asymptotic questions for number fields and elliptic curves. We will then focus on one method that has been successful, especially in recent years, in studying some of these problems: a combination of explicit constructions of moduli spaces, geometry-of-numbers techniques, and analytic number theory. </div>
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ScientificMathematicsTopologyFri, 28 Jun 2019 23:50:15 +0000root739 at http://www.mathtube.orgStable cohomology of complements of discriminants
http://www.mathtube.org/lecture/video/stable-cohomology-complements-discriminants
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Speaker: </div>
Orsola Tommasi </div>
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Date: </div>
<span class="date-display-single">Thu, Jun 13, 2019</span> </div>
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Location: </div>
PIMS, University of British Columbia </div>
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Workshop on Arithmetic Topology </div>
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The discriminant of a space of functions is the closed subset consisting of the functions which are singular in some sense. For instance, for complex polynomials in one variable the discriminant is the locus of polynomials with multiple roots. In this special case, it is known by work of Arnol'd that the cohomology of the complement of the discriminant stabilizes when the degree of the polynomials grows, in the sense that the k-th cohomology group of the space of polynomials without multiple roots is independent of the degree of the polynomials considered. A more general set-up is to consider the space of non-singular sections of a very ample line bundle on a fixed non-singular variety. In this case, Vakil and Wood proved a stabilization behaviour for the class of complements of discriminants in the Grothendieck group of varieties. In this talk, I will discuss a topological approach for obtaining the cohomological counterpart of Vakil and Wood's result and describe stable cohomology explicitly for the space of complex homogeneous polynomials in a fixed number of variables and for spaces of smooth divisors on an algebraic curve. </div>
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ScientificMathematicsTopologyFri, 28 Jun 2019 22:33:49 +0000root737 at http://www.mathtube.orgThe circle method and the cohomology of moduli spaces of rational curves
http://www.mathtube.org/lecture/video/circle-method-and-cohomology-moduli-spaces-rational-curves
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Speaker: </div>
Will Sawin </div>
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<span class="date-display-single">Thu, Jun 13, 2019</span> </div>
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Location: </div>
PIMS, University of British Columbia </div>
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Workshop on Arithmetic Topology </div>
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The cohomology of the space of degree d holomorphic maps from the complex projective line to a sufficiently nice algebraic variety is expected to stabilize as d goes to infinity. The limit is expected to be the cohomology of the double loop space, i.e. the space of degree d continuous maps from the sphere to that variety. This was shown for projective space by Segal, and there has been further subsequent work. In joint work with Tim Browning, we give a new approach to the problem for smooth affine hypersurfaces of low degree (which should also work for projective hypersurfaces, complete intersections, and/or higher genus curves), based on methods from analytic number theory. We take an argument of Birch that solves the number-theoretic analogue of this problem and translate it, step by step, into the language of ell-adic sheaf theory using the sheaf-function dictionary. This produces a spectral sequence that computes the cohomology, whose degeneration would imply that the rational compactly-supported cohomology matches that of the double loop space. </div>
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ScientificMathematicsTopologyFri, 28 Jun 2019 18:07:56 +0000root736 at http://www.mathtube.org