Groups, Rings, Lie and Hopf Algebras IV
2022-05-30 - 2022-06-02 | Memorial University (St. John’s Campus), St. John's, Newfoundland and Labrador, Canada
The aim of this workshop is to discuss the current state of research in several interrelated areas of algebra. The first three workshops with the same title were held on the St. John’s campus of Memorial University (MUN) in 2001 and at the Bonne Bay Marine Station of MUN in Gros Morne National Park in 2007 and 2012. The current workshop is organized by the Atlantic Algebra Centre (AAC) of MUN in the framework of the collaborative research group “Groups, Rings, Lie and Hopf Algebras” of the Atlantic Association for Research in the Mathematical Sciences (AARMS). It will immediately precede the summer meeting of Canadian Mathematical Society, which will be held in St. Johns from June 3 to June 6.

Mathematical foundations of scientific machine learning
2022-06-01 - 2022-06-03 | Memorial University (St. John’s Campus), St. John's, Newfoundland and Labrador, Canada
Workshop hosted by the AARMS CRG in Scientific Machine Learning. Remote participation via Webex possible. Full program and connection details: Program

Public Lecture: Dr. Ivan Shestakov
2022-06-01 19:00 - 20:00 UTC | Memorial University (St. John’s Campus), St. John's, Newfoundland and Labrador, Canada
Dr. Ivan Shestakov will be visiting St. John’s, NL, from May 29 to June 3, as a guest of the Atlantic Algebra Centre in the department of Mathematics and Statistics at Memorial University and as an AARMS Distinguished Lecturer. While there, Dr. Shestakov will give a plenary talk to the International Workshop “Groups, Rings, Lie and Hopf Algebras IV”. The title of the talk is “Non-matrix Varieties and Coordinatization Theorems”. Dr. Shestakov will also deliver a public lecture as described below.
Tame and Wild Automorphisms of Free Algebras
The notion of automorphism captures the idea of symmetry in mathematics. More precisely, an automorphism of an object is an invertible transformation that preserves the object’s structure. Many important objects in algebra possess natural examples of such transformations, which are referred to as elementary automorphisms. For such an object, an automorphism is called tame if it can be represented as a composition of elementary automorphisms, otherwise it is called wild.
It is known that the automorphisms of polynomial algebra and of free associative algebra are tame in case of two generators while in case of three generators there exist wild automorphisms.
In our talk, we will discuss known results and open problems on tame and wild automorphisms in various classes of algebras.
Speaker Bio
Ivan Shestakov was born on August 13, 1947, in Zaval’, Irkutsk region, Russia. After graduating from the Physical-Mathematical School in Novosibirsk, he entered Novosibirsk University in 1965. There he obtained his first results in algebra, under the guidance of professors K. Zhevlakov and A. Shirshov. His Masters thesis “On a Class of Non-commutative Jordan Rings” was awarded the Medal of the Academy of Sciences of USSR for students. In 1970 Shestakov graduated from Novosibirsk University and entered as a researcher the Sobolev Institute of Mathematics. In 1973 he received his Ph.D. from Novosibirsk University, and in 1978 he earned the Doctor of Sciences from the Sobolev Institute of Mathematics for the work “Free Alternative Algebras”. In 1974 Shestakov became a professor of the Novosibirsk State University. Since 1999 he has held a position of Full Professor at the University of Sao Paulo. In 2007 he was awarded, jointly with U. Umirbaev, the E. H. Moore Research Article Prize of the AMS for the solution of the Nagata problem on polynomial automorphisms. In 2009 Shestakov was elected to the Brazilian Academy of Sciences, and in 2010 he was awarded the “Ordem de Merito Scientifico” by the president of Brazil. In 2016 Shestakov was elected a Fellow of the AMS, and in 2017 he was awarded the Gold Medal “For Great Contributions to Mathematics” by the Sobolev Institute of Mathematics (Novosibirsk, Russia). Shestakov’s interests lie in the Ring Theory and Combinatorial Algebra. He has focused on the structure and representations of non-associative algebras and superalgebras, PIalgebras, free algebras and their automorphisms.
Connection Details
To attend in person:
Room EN-2006, S. J. Carew Building
Memorial University
240 Prince Phillip Drive
St. John’s, NL
To attend virtually:
Connection details will be published at:
https://www.mun.ca/aac/

Session on Design Theory and Graph Decompositions at the 2022 Summer Meeting of the Canadian Mathematical Society
2022-06-03 - 2022-06-06 | Memorial University (St. John’s Campus), St. John's, Newfoundland and Labrador, Canada
Combinatorial design theory has a history dating back to the 18th century when Leonhard Euler pondered the existence of orthogonal pairs of Latin squares. This session will showcase recent results in topics such as classical designs, cycle systems, graph decompositions, Latin squares and other aspects of design theory by bringing together leading and emerging researchers in the field to share their recent results, techniques, and applications.

Applied and geometric analysis--A Session at the CMS Summer meeting
2022-06-06 | Memorial University (St. John’s Campus), St. John's, Newfoundland and Labrador, Canada
This proposed scientific session at CMS Summer Meeting at Memorial University, June 3-6, 2022, will bring together several researchers to present their recent results and discuss further developments of applied geometric analysis.

AARMS Geophysical Inverse Problems Discussion
2022-06-10 01:30 - 14:30 UTC | Zoom seminar
Gündoğdu & Candansayar, 2018, Three-dimensional regularized inversion of DC resistivity data with different stabilizing functionals.
Also available on the author’s ResearchGate page:

https://www.researchgate.net/publication/326068036_Three-dimensional_regularized_inversion_of_DC_resistivity_data_with_different_stabilizing_functionals

This paper compares several regularization functionals that have appeared in geophysical inversion literature. It can provide an overview for us before perhaps looking at some others in more detail, if needed.

Friday, June 10, 2022 @ 1:30 pm – 2:30 pm (Atlantic time)

Stinson66 - New Advances in Designs, Codes and Cryptography
2022-06-13 - 2022-06-17 | Fields Institute, 222 College St., Toronto, Ontario, M5T 3J1, Canada
This conference will celebrate Doug Stinson’s 66th birthday and highlight his contributions to the fields of designs, codes, cryptography, and their connections. The goal is to explore recent developments, open problems and conjectures in combinatorial design theory along with applications to related areas including codes, cryptography, networks, and algorithms. We intend to bring together leading researchers from around the world, along with graduate students, postdocs and other early-career researchers. The conference will consist of invited talks only and will provide ample opportunity for discussion and collaboration among the participants.

AARMS Geophysical Inverse Problems Discussion
2022-06-24 13:30 - 14:30 UTC | Zoom seminar
Farquharson & Oldenburg, 2004, A comparison of automatic techniques for estimating the regularization parameter in non-linear inverse problems.
Also available here:

https://gif.eos.ubc.ca/sites/default/files/Farquharson_regparam_04.pdf

This paper compares some common approaches for choosing the value of the regularization parameter in underdetermined, minimum-structure-type inverse problems. It can provide an overview for us before looking at more recent ideas.
Friday, June 24, 2022 @ 1:30 pm – 2:30 pm (Atlantic time)

Junior Math and Computer Science Camp
2022-07-04 - 2022-07-08 | Acadia University, Wolfville, Nova Scotia, Canada
This week-long day camp is an opportunity for students entering grades 5 or 6 in the Annapolis Valley to participate in fun and enriching science-based activities with Acadia faculty and students to develop their curiosity and enjoyment of math and computer science. It represents an important piece of a multi-year plan to develop the science skills of young students in the Annapolis Valley by bringing young students into the Acadia University outreach program. This will begin the process of positively engaging students with math and computer science at a critical time in their education. Bursaries are provided for those who qualify for financial assistance.

Computational Aspects in Finance and Actuarial Sciences
2022-07-08 - 2022-07-09 | University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada
The AARMS CRG Conference on Computational Aspects in Finance and Actuarial Sciences will be held July 8-9 in PEI, Canada. This conference is mainly hosted by the Atlantic Association for Research in Mathematical Sciences (AARMS) collaborative research group (CRG) and the School of Mathematical and Computational Sciences (SMCS) at University of Prince Edward Island (UPEI), Canada, and is a unique venue that brings together leaders in finance, and actuarial sciences, across disciplines, and across borders, tackling very important and timely topics in finance and actuarial sciences. Our intention for this conference is to have a broad scope in terms of applications in Finance and Actuarial Sciences but we would like to put emphasis on numerical and computational issues (including trendy topics such as machine learning algorithms in finance and insurance, but also more traditional methods such as numerical solutions for PDEs, Monte Carlo simulations, etc). The conference will include a dynamic program with high quality speakers focusing on innovative research, policy discussions, and business challenges and successes.
ZOOM link: https://us06web.zoom.us/u/kUOl82t1s

Canadian Undergraduate Mathematics Conference / Congrès canadien des étudiant(e)s en mathématiques
2022-07-13 - 2022-07-17 | Université Laval, 2325 Rue de l'Université, Québec, Québec, G1V 0A6, Canada
The Canadian Undergraduate Mathematics Conference (CUMC) is a national conference organized each summer by undergraduate students for undergraduate students at different institutions across Canada.
The CUMC is an opportunity for students to explore mathematics outside their usual surroundings and spark their interest in areas they have not yet been exposed to. Indeed, the core of the gathering consists of a series of talks given by participants. The conference therefore provides a unique chance for students to present what they find most fascinating and exciting, as well as to practice their expository skills in an inclusive and noncompetitive environment. As a national conference, the CUMC is a bilingual event. Moreover, the event seeks to promote diversity within the field of mathematics itself, by offering keynote lectures in both pure and applied fields.
The CUMC is primarily organised by a local organising committee at the host institution, under the aegis of Studc.

AARMS Geophysical Inverse Problems Discussion
2022-07-15 13:30 - 14:30 UTC | Zoom seminar
Friday, July 15, 2022 @ 1:30 pm – 2:30 pm (Atlantic time)
Bijani et al., 2017, Physical-property-, lithology- and surface-geometry-based joint inversion using Pareto Multi-Objective Global Optimization.
If you are unable to access the paper through that link, please email the organizer (and co-author on the paper) for a copy (plelievre@mta.ca).
This paper introduces the concept of multi-objective optimization and Pareto-optimality. In this work, instead of attempting to select a single value for the regularization parameter, the methods sample the entire Pareto-curve (Tikhonov curve), or for more than two objective functions the Pareto-(hyper)surface. The challenge is then deciding how to visualize and otherwise explore all the possible models provided, extract useful information from them, and make reasonable interpretations.
Connection details will be available on the organizer’s website.

AARMS Geophysical Inverse Problems Discussion
2022-07-29 13:30 - 14:30 UTC | Online via Zoom
Lelièvre et al., 2012, Joint inversion of seismic traveltimes and gravity data on unstructured grids with application to mineral exploration.
https://library.seg.org/doi/10.1190/geo2011-0154.1

If you are unable to access the paper through that link, please email the organizer (and co-author on the paper) for a copy (plelievre@mta.ca).
This paper looks at various different methods to enforce the similarity of the different models in a joint inversion. This paper will help us discuss previous themes in relation to joint inversion, including the deterioration of numerical behavior for particular objective functions, constructing piecewise-constant models, and determining the value of the regularization parameter(s).

Friday, July 29, 2022 @ 1:30 pm – 2:30 pm (Atlantic time)

Connection details will be published on the organizer’s website:
https://www.esd.mun.ca/~peter/AARMS-CRG.html

Symmetry, Invariants, and their Applications: A Celebration of Peter Olver’s 70th Birthday
2022-08-03 - 2022-08-05 | Halifax, Halifax, Nova Scotia, Canada
This is a proposal for a workshop on symmetry, invariants, and their applications in celebration of Peter Olver’s 70th birthday. Transformation and groups are an omnipresent concept in nature, science, and art. Many biological, chemical, physical, or man-made structures exhibit symmetries as a fundamental design principle or as an essential aspect of their functioning. Symmetry groups also occur in a wide variety of modern applications including computer vision, archaeology, numerical integration, and neural networks, differential equations, geometry, and applied mathematics.
During his prolific career, Peter J. Olver played an important role in the development of symmetry group methods to differential equations, geometry, and applied mathematics.The purpose of the workshop is to bring together leading experts, promising younger researchers, and graduate students from around the world to assess the rapid advances occurring in the field of symmetries and invariants, and to evaluate the most promising directions of future developments.

Intersection of Microlocal Analysis, Harmonic Analysis, and Inverse Problems: A conference in honor of Allan Greenleaf
2022-08-15 - 2022-08-17 | University of Rochester, 500 Joseph C. Wilson Blvd, Rochester, NY, United States
The objective of the conference is to bring together an international group of experts in three areas: microlocal analysis, inverse problems and harmonic analysis. There will be 19 internationally recognized researchers in those subjects, each invited to give a lecture. There has recently been great progress in all these areas, with mutual benefits, and no end in sight. With this conference we hope to foster interaction and collaboration among speakers and other participants from the three different areas. Furthermore, the conference will take the opportunity to honor the research achievements of Professor Allan Greenleaf, who has made fundamental contributions to many of the topics covered by this conference.

East Coast Combinatorics Conference
2022-08-17 - 2022-08-18 | University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada
The East Coast Combinatorics Conference is an annual conference designed to support and bring together researchers in mathematics and computer science interested in all aspects of combinatorics. A unique feature is the workshop-like atmosphere which encourages active collaboration and participation of faculty and students while highlighting major theoretical advances and applications in the area. In addition to plenary talks, the conference features contributed talks presented by faculty, students, and post-docs.

34th Canadian Conference on Computational Geometry
2022-08-25 - 2022-08-27 | Ryerson University, Toronto, Ontario, Canada
The Canadian Conference on Computational Geometry (CCCG) is a forum to disseminate and discuss theoretical and applied results in discrete and computational geometry.
Computational geometry is concerned with the design of efficient algorithms, the development of software, and the study of the mathematical foundations of computational problems whose formulation involves geometric constraints. The field is motivated by problems from a broad range of application areas, as diverse as computer graphics and animation, computer vision, computer-aided design and manufacturing, geographic information systems, pattern recognition, wireless communications, robotics, protein folding, urban planning, graph drawing, or statistical analysis. The 34th Canadian Conference on Computational Geometry will take place in August 2022 in Toronto, ON.

Science Atlantic Mathematics, Statistics, and Computer Science Conference
2022-10-21 - 2022-10-22 | Mount Allison University, Sackville, New Brunswick, Canada
The Science Atlantic Mathematics, Statistics, and Computer Science Conference is held each October and provides an opportunity for students to present their research and to learn about other undergraduate research projects across the region in a supportive and inclusive environment. Undergraduate students are also able to participate in team-based mathematics and programming competitions. The conference additionally provides a valuable opportunity for undergraduate students to meet potential graduate supervisors, and is the only venue for faculty members from across Atlantic Canada to network and share ideas and information related to research and mentorship.

University of New Brunswick Data Challenge 2022
2022-11-18 | University of New Brunswick (Fredericton Campus), Fredericton, New Brunswick, Canada
The Data Challenge will bring together three competitive events, Data Visualization (7th Annual), Data Analytics (3rd Annual), and Data Sprint (3rd Annual) on Nov. 18, 2022, in a hybrid format – virtually and in person! Take up the challenge and demonstrate the power of data, with the flexibility to take part remotely.
Participants and teams will have the chance to showcase their ability to tell a story driven by data in three unique competitive formats. Teams can participate in all three competitive events. It is an ideal setting for citizens to get engaged, meet leaders in academia, government, and private organizations, and explore the world of data science.

Atlantic Graph Theory Seminar: Sebastian Cioaba, University of Delaware
2022-11-30 15:30 - 16:30 UTC | Online via Zoom
Addressing graphs and hypergraphs
In 1970s, Ron Graham and Henry Pollak introduced the notion of graph addressing which is a labeling of the vertices of an undirected graph by words of the same length over the alphabet {0,1,*} such that the distance between any two vertices equals the number of positions in their labels/addresses where one vertex has a 0 and the other one has a 1. The minimum of length of such words has been investigated by various people and is closely related to the partition of the edge set of the graph into bicliques (complete bipartite subgraphs). In this talk, I will describe some recent results related to this parameter for various families of graphs and the corresponding problem for hypergraphs.
Zoom info:

https://us02web.zoom.us/j/87564743456?pwd=[REDACTED]
Meeting ID: 875 6474 3456
Passcode: [REDACTED]

The 19th Seminar on Commutative Algebra and related topics
2023-01-07 - 2023-01-12 | Institute for Research in Fundamental Sciences (IPM) Tehran, Iran, Tehran, Iran, Islamic Republic of
Every year the school of mathematics of IPM-Tehran organizes a seminar and workshop to introduce the research topics in the main streams of “Algebraic Geometry, Commutative algebra and Combinatorial commutative algebra” to young researchers and PhD students, and encourage them to collaborate in teams led by well-known mathematicians in this area. This year we have paid special attention to inviting regional speakers, as well as international leaders. Our list of speakers highlights female mathematicians, and the areas represented are those in which there is regional expertise, hopefully leading to new collaborations.
The conference is preceded by a workshop on Lefschetz properties and connections to algebra, geometry and combinatorics. The workshop will feature the leading questions in the area, and the lectures will be delivered by some of the main players in this field.

Atlantic Graph Theory Seminar: Pawel Pralat, Metropolitan University of Toronto
2023-01-11 15:30 - 16:30 UTC | Online via Zoom
An Unsupervised Framework for Comparing Graph Embeddings
The goal of many machine learning applications is to make predictions or discover new patterns using graph-structured data as feature information. In order to extract useful structural information from graphs, one might want to try to embed it in a geometric space by assigning coordinates to each node such that nearby nodes are more likely to share an edge than those far from each other. There are many embedding algorithms (based on techniques from linear algebra, random walks, or deep learning) and the list constantly grows. As a result, selecting the best embedding is a challenging task and very often requires domain experts. Our general framework assigns the divergence score to each embedding which, in an unsupervised learning fashion, distinguishes good from bad embeddings. In order to benchmark embeddings, we generalize the Chung-Lu random graph model to incorporate geometry.

Join Zoom Meeting
https://us02web.zoom.us/j/82306017918?pwd=[REDACTED]

Meeting ID: 823 0601 7918
Passcode: [REDACTED]

Dalhousie-AARMS AAMP Seminar: Andrea Bertozzi (UCLA)
2023-01-13 16:00 - 17:00 (America/Halifax) | Dalhousie University, Halifax, Nova Scotia, Canada
Title: Energy Minimizing Surface Tension Configurations for Microparticles
Abstract: An important area of microfluidics is the creation and manipulation of small droplets. This is commonly done using microchannels or electrowetting. Recently a new method is proposed to create templated droplets using amphiphilic microparticles. These particles are observed to hold nearly equal volumes of aqueous liquid when dispersed in an oil–water mixture. However a theory for this behavior is lacking. In this paper, we present a mathematical model based on minimizing the surface tension energy of a system of particles. By analyzing this model, we demonstrate that certain key properties of the particle guarantee the formation of small droplets within a volume range unique to the particle. We also look at statistical dynamics of pairwise exchange of fluids between particles for which the system can reach equilibrium. We show examples of how such particles are useful for applications such asbiological assays and measurement of chemical secretions from single cells.

The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom and in Chase 227. If you would like to attend, please email the organizers for connection details.

Atlantic Graph Theory Seminar: Jane (Pu) Gao, University of Waterloo
2023-01-18 15:30 - 16:30 UTC | Online via Zoom
Conditions for perfect matchings in random sparse bipartite graphs
Given a uniformly random sparse matrix A, with specified number of nonzero entries in columns and rows, we determine when A has full row rank over a finite field. As a corollary, by considering A as the adjacency matrix of a bipartite graph, our result determines the conditions for the existence of a perfect matching in various models of random sparse bipartite graphs. We will explore some useful insight from statistical physics that guides our probabilistic combinatorial proof. This is joint work with Coja-Oghlan, Hahn-Klimroth, Lee, Mueller and Rolvien.

Join Zoom Meeting
https://us02web.zoom.us/j/82306017918?pwd=[REDACTED]

Meeting ID: 823 0601 7918
Passcode: [REDACTED]

Dalhousie-AARMS AAMP Seminar: Chamsol Park (Johns Hopkins University)
2023-01-20 16:00 - 17:00 (America/Halifax) | Dalhousie University, Halifax, Nova Scotia, Canada
Title: Eigenfunction restriction estimates on curves with nonvanishing geodesic curvatures

Abstract: Studying eigenfunctions of the Laplace-Beltrami operator on compact Riemannian manifolds (without boundary) is one of the interesting topics in Harmonic Analysis. One way to study them is to consider the L^p estimates of the eigenfunctions restricted to submanifolds. In this talk, we briefly summarize previous results and would like to talk about the logarithmic improved analogue for the restriction to curves with nonvanishing geodesic curvatures, in the presence of nonpositive sectional curvatures in the manifolds. If time permits, we will discuss some applications and open problems for the Schrodinger counterparts.

The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom and in Chase 227. If you would like to attend, please email the organizers for connection details.

Dalhousie-AARMS AAMP Seminar: Alex Barnett (Flatiron Institute, NYC)
2023-01-27 16:00 - 17:00 (America/Halifax) | Dalhousie University, Halifax, Nova Scotia, Canada
Title: Equispaced Fourier representations for efficient Gaussian process regression from a billion data pointsAbstract: Gaussian process regression is widely used in geostatistics, time-series analysis, and machine learning. It infers an unknown continuous function in a principled fashion from noisy measurements at $N$ scattered data points. The prior on the function is Gaussian, with covariance given by some user-chosen translationally invariantkernel. Yet $N$ has been limited to about $10^6$, even with modern low-rank methods. Focusing on low spatial dimension (1–3), we present a GP regression method using kernel approximation by an equispaced quadrature grid in the Fourier domain. This enables the iterative solution of a smaller Toeplitz linear system, exploiting both the FFT and the nonuniform FFT to give ${mathcal O}(N)$ cost. The result is often one to two orders of magnitude faster than state of the art methods, and enables cheap massive-scale regressions. For example, for a 2D Mat’ern-3/2 kernel and $N = 10^9$ points, the posterior mean function is found to 3-digit accuracy in two minutes on a desktop.Joint work with Philip Greengard (Columbia) and Manas Rachh (Flatiron Institute)
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over either Zoom and/or in Chase 227 depending on the speaker. If you would like to attend, please email the organizers for connection details.

Atlantic Graph Theory Seminar: Jason Brown, Dalhousie University
2023-02-08 15:30 - 16:30 UTC | Online via Zoom
Colourings, Polynomials and Roots
A lot has happened since graph colourings first arose as an applied problem in cartography – do four colours always suffice to distinguish countries when colouring a map? Along the way to the proof, the related enumeration function to count the number of k-colourings was proposed. While the latter didn’t help much in the quest for the Four Colour Theorem, it did lead to a fascinating branch of graph theory, namely chromatic polynomials. While polynomials are the simplest of functions, their properties can take you deep within mathematics. In this talk I will describe some recent result on chromatic polynomials and their offshoots, connecting to commutative algebra as well as real and complex analysis. And on our trip, we visit with some old friends, including Charles Hermite, Jacques Sturm, and Carl Gauss.
Meeting ID: 831 4765 9865
Passcode: [REDACTED]

Dalhousie-AARMS AAMP Seminar: Victor Ivrii (U. Toronto)
2023-02-10 16:00 - 17:00 (America/Halifax) | Dalhousie University, Halifax, Nova Scotia, Canada
Title + Abstract: TBD
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over either Zoom and/or in Chase 227 depending on the speaker. If you would like to attend, please email the organizers for connection details.

Atlantic Graph Theory Seminar: Jérémie Turcotte, Université de Montréal
2023-02-15 15:30 - 16:30 UTC | Online via Zoom
Progress towards the Burning Number Conjecture
The burning number b(G) of a graph G is the smallest integer k such that G can be covered by k balls of radii respectively 0,…,k-1, and was introduced independently by Brandenburg and Scott at Intel as a transmission problem on processors and Bonato, Janssen and Roshanbin as a model for the spread of information in social networks. The Burning Number Conjecture claims that b(G)<=lceilsqrt{n}rceil, where n is the number of vertices of G. This bound is tight for paths. The previous best bound for this problem, by Bastide et al., was b(G)<= sqrt{frac{4n}{3}}+1. We prove that the Burning Number Conjecture holds asymptotically, that is b(G)<= (1+o(1))sqrt{n}. Following a brief introduction to graph burning, this talk will focus on the general ideas behind the proof.
Meeting ID: 885 9352 1895
Passcode: [REDACTED]

Minicourse: Group Graded Azumaya Algebras and Generic Constructions
2023-02-17 11:00 - 2023-02-22 12:00 UTC | Memorial University (St. John’s Campus), St. John's, Newfoundland and Labrador, Canada
Taught by Professor Eli Aljadeff, Technion University, Israel
The main theme of this mini-course is gradings by finite groups on finite-dimensional algebras. Similar to the classical situation of ungraded algebras, we will be interested in finite-dimensional graded simple algebras and finite-dimensional graded division algebras. An important role is played by a generalization of central simple algebras, called Azumaya algebras.
Our main tool will be polynomial identities and, in particular, graded polynomial identities. This tool will allow us to construct generic graded Azumaya algebras.
In the first lecture of the mini-course, as a part of the motivation to discuss group graded algebras, I will recall some classical topics such as division algebras, Brauer groups, crossed products and Galois cohomology. Then I will introduce G-graded polynomial identities, where G is a finite group, and discuss generic constructions. In particular, for an arbitrary finite-dimensional G-graded simple algebra A over an algebraically closed field F of characteristic 0, I will construct a generic G-graded Azumaya algebra from which one can obtain by specialization all forms of A in the sense of Galois descent.
As a key application, I will discuss the following problem. It is not difficult to see that for any finite group G, finite-dimensional G-graded division algebras are G-graded simple and they remain G-graded simple upon any extension of the field of scalars.
We will be interested in the opposite direction. Unlike the situation in the ungraded case, where the algebras of n × n matrices always admit forms which are division algebras, this is not generally true in the setting of G-graded algebras.
Suppose that A is a finite-dimensional G-graded simple algebra over an algebraically closed field F. One of the goals of these lectures is to provide necessary and sufficient conditions on the graded structure of A under which A admits forms that are G-graded division algebras. In particular we show that A must be a G-graded simple algebra for which the corresponding generic G-graded simple algebra is a G-graded division algebra.
The lectures will be delivered during three time periods, as shown below. They will take place at the St. John’s campus of Memorial University and will be broadcast via Webex. All the times are in Newfoundland Time (NST=UTC-3:30).
Friday, February 17, 11-12 am, room A-1045/1046
Monday, February 20, 11-12 am, room A-1045/1046
Wednesday, February 22, 11-12 am, room A-1045/1046
The lectures will be available online via Webex. Contact the organizer for details
