Goal
The Fields Academy shared graduate courses program increases the range of advanced mathematics courses available to students at Ontario universities.
Instructors
Courses taught through Fields Academy are selected from courses offered at the Fields Institute’s Principal Sponsoring Universities. There will be a call for courses in each December for the following academic year. Instructors are invited, with the approval of their Department Chair, to submit their course. The selection of courses will be decided by the Deputy Director in consultation with an Advisory Committee.
Students巴西四级带毛电影无删在线巴西四级带毛电影无删在线,八一影院最新安卓版下载八一影院最新安卓版下载,八戒私人影院网站 视频八戒私人影院网站 视频
International and students who do not attend any of our 巴西四级带毛电影无删在线巴西四级带毛电影无删在线,八一影院最新安卓版下载八一影院最新安卓版下载,八戒私人影院网站 视频八戒私人影院网站 视频Principal Sponsoring Universities (Carleton University, McMaster University, Queen's University, Ryerson University, University of Ottawa, University of Toronto, University of Waterloo, Western University and York University) have to pay the registration fee via this page.
Students wishing to take one of these courses for credit should contact the Graduate Chair (or equivalent) of their own department to make arrangements. One option is to follow Ontario's standardized procedure allowing graduate students to take courses at other universities as described here (under the tab "Ontario Visiting Graduate Students"): /resources/graduate-studies/
Courses (Winter 2021)
Graduate Model Theory | McMaster University
Instructor: Prof. Bradd Hart
Email: hartb@mcmaster.ca
Application Deadline: January 19th, 2021
Lecture Times: Tuesdays and Wednesdays | 11:00 am - 12:30 pm
Course Dates: January 12th - April 7th, 2021
Registration Link: /meeting/register/tJcoduuoqTkqGNVkzSMZUJZimaOXbVgTmaJ_
Course Overview
This course will be a classical model theory course which will touch on all the basic themes with a modern lens. In addition to emphasizing standard results like completeness and compactness, the framework will be broadened from the start to include the multi-sorted setting which will enable a naturual discussion of quotient objects via imaginaries. Abstract model theoretic theorems such as the Beth definability theorem and Lindstrom's characterization of first order logic will be included in a practical setting. Applications of the Henkin construction as well as the abstract role of ultraproducts will be emphasized. The course will end with a proof of Morley's categoricity theorem in the style of Baldwin-Lachlan with some emphasis on the geometric nature of modern treatments.
Introduction to Algebraic Geometry | University of Ottawa
Instructor: Prof. Kirill Zainoulline
Email:
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Application Deadline: January 17th, 2021
Lecture Times: Mondays | 11:30 am - 12:50 pm and Wednesdays | 10:00 am - 11:20 am
Course Dates: January 11th - April 12th, 2021
Registration Link: /MAT4154/?page_id=322
Course Overview
A brief overview of commutative algebra: rings and ideals, Nakayama's Lemma, localization, Krull-dimension, direct-limits, integral dependence. Toward algebraic varieties: Regular functions, algebraic sets, Hilbert's Nullstellensatz, Zariski topology, ringed spaces, affine and projective varieties. Toward sheaves and group schemes: functors of points, Grothendieck topologies, representable functors, group schemes, tori, Grassmannians, torsors and twisted forms, quadrics and Severi-Brauer varieties.
Mathematical Cell Biology | University of Waterloo
Instructors: Prof. Sue Ann Campbell, Prof. Brian Ingalls
Emails: sacampbell@uwaterloo.ca, bingalls@uwaterloo.ca
Application Deadline: January 19th, 2021
Lecture Times: Tuesdays and Thursdays | 10:30 am - 11:50 am
Course Dates: January 12th - April 13th, 2021
Registration Link: /meeting/register/tJUldeuvqTkjH9FfRnIfKWfKVajX1dy1ZL30
Course Overview
This course will cover dynamic mathematical modelling of biological processes at the cellular level. The first half of the course will treat intracellular networks: metabolism, signal transduction, and genetic regulatory networks from the systems biology perspective. The second half of the course will treat biological neural networks, from single neurons to large networks. Modelling in the course will be carried out primarily through ordinary differential equations; analysis will involve application of dynamical systems tools and simulation.
Symplectic Geometry | University of Waterloo
Instructor: Prof. Ben Webster
Email: ben.webster@uwaterloo.ca
Application Deadline: January 18th, 2021
Lecture Times: Mondays and Wednesdays | 1:00 pm - 2:30 pm
Course Dates: January 11 - April 12, 2021
Registration Link: /meeting/register/tJcud-uqqD8jGdFAiuhtamPqtArOUQUjpGW_
Course Overview
This class covers the basic theory of symplectic manifolds. Symplectic structures play a key role in modern mathematics and physics. We will discuss their basic local theory (in particular, the Darboux theorem), connections to complex and Kähler geometry, Hamiltonian mechanics, moment maps and symplectic reduction, and some additional topics, such as toric varieties, hyperkähler structures, quantization, Fukaya categories and mirror symmetry.
Introduction to Spectral Geometry | Western University
Instructor: Prof. Masoud Khalkhali
Email: masoud@uwo.ca
Application Deadline: January 18th, 2021
Lecture Times: Mondays and Wednesdays | 2:00 pm - 3:30 pm
Course Dates: January 11th - April 7th, 2021
Registration Link: /meeting/register/tJUldeGorj8oEtdW8GvRXn0El34Ojb-O2r4x
Course Overview
One of the central questions of spectral geometry is to know how much of the geometry and topology of a Riemannian manifold can be recovered from its Laplace spectrum. For example, is it true that isospectral manifolds are isometric? The essence of this question was captured in the title of a famous article by Marc Kac "Can one hear the shape of a drum?". Topics to be covered: spectral decomposition of $L^2 (M)$, direct and inverse spectral problems, Minakshisundaram-Pleijel asymptotic expansion of the heat kernel, Weyl's asymptotic law, lattice theta functions and Milnor's counterexample, Counterexamples of Gordon-Web-Wolpert, spectral zeta functions, trace formulas of Poisson and Selberg.
Massive C*-algebras | York University
Instructor: 巴西四级带毛电影无删在线巴西四级带毛电影无删在线,八一影院最新安卓版下载八一影院最新安卓版下载,八戒私人影院网站 视频八戒私人影院网站 视频Prof. Ilijas Farah
Email: ifarah@yorku.ca
Application Deadline: January 19th, 2021
Lecture Times: Mondays and Fridays | 9:00 am - 10:30 am
Course Dates: January 11th - April 9th, 2021
Registration Link: /meeting/register/tJwlfuuprDkvHNIoT_XVFfvM5M8Nc7Ujvu50
Course Overview
The route to understanding separable C*-algebras frequently involves a detour via nonseparable C*-algebras, such as the Calkin algebra, the asymptotic sequence algebras, ultrapowers, and ultraproducts. Some basic ideas from logic can be used to analyze these massive C*-algebras. Among other things, we will see that the existence of outer automorphisms of the Calkin algebra depends on the set-theoretic axioms.
