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UBC cIRcle BIRS Workshop Lecture Videos Logo
A necessary condition for global rigidity
Banff International Research Station for Mathematical Innovation and Discovery
Guler, Hakan — Non UBC Unreviewed Author affiliation: Queen Mary, University of London Graduate http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
Multiplicative functions and nilsequences
Banff International Research Station for Mathematical Innovation and Discovery
Matthiesen, Lilian — Faculty Non UBC Unreviewed Author affiliation: Leibniz Universität Hannover http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
Local discontinuous Galerkin methods for phase field models
Banff International Research Station for Mathematical Innovation and Discovery
Xu, Yan — Non UBC Unreviewed Author affiliation: University of Science and Technology of China Faculty http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
Applications of Superconformal Representation Theory
Banff International Research Station for Mathematical Innovation and Discovery
Cordova, Clay — Local operators in supersymmetric conformal field theory are in representations of the super- conformal group. In this talk, I will briefly review this representation theory and apply it to shed light on some basic questions such as: Are there (N,0) superconformal field theories? Do the (2,0) theories have continuous parameters or global symmetries? Why is the (2,0) theory on a circle described by 5d Super-Yang-Mills? How can we understand the RG flow of the (2,0) theory on its moduli space? Non UBC Unreviewed Author affiliation: Harvard University Postdoctoral http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
Quivers of finite mutation type
Banff International Research Station for Mathematical Innovation and Discovery
Shapiro, Michael — Quiver mutations play important role in definition of cluster algebra and also appeared independently as Seiberg duality in mathematical physics. In this talk I will discuss quivers with finite mutation class, more exactly, classification result and its application. ​This is a joint work with A.Felikson and P.Tumarkin. Non UBC Unreviewed Author affiliation: Michigan State University Faculty http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
Mutation via Hovey twin cotorsion pairs and model structures in extriangulated categories
Banff International Research Station for Mathematical Innovation and Discovery
Nakaoka, Hiroyuki — Non UBC We give a simultaneous generalization of exact categories and triangulated categories, which is suitable for considering cotorsion pairs, and which we call extriangulated categories. Extension-closed, full subcategories of triangulated categories are examples of extriangulated categories. We give a bijective correspondence between some pairs of cotorsion pairs which we call Hovey twin cotorsion pairs, and admissible model structures. As a consequence, these model structures relate certain localizations with certain ideal quotients, via the homotopy category which can be given a triangulated structure. This gives a natural framework to formulate reduction and mutation of cotorsion pairs, applicable to both exact categories and triangulated categories. These results can be thought of as arguments towards the view that extriangulated categories are a convenient setup for writing down proofs which apply to both exact categories and (extension-closed subcategories of) triangulated categories. This is a joint work with Yann Palu. Faculty Author affiliation: Kagoshima University Unreviewed http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
The Telescope conjecture for algebraic stacks
Banff International Research Station for Mathematical Innovation and Discovery
Hall, Jack — Let T be a triangulated category. A basic question is the classification of the triangulated subcategories of T. The interest in this question stemmed from the work of Hopkins who connected it to the Telescope conjecture in algebraic topology. Over the last two decades, spurred by work of Neeman, there has been interest in this from the perspective of algebraic geometry. Most recently, this has been considered by Antieau, Stevenson, Balmer-Favi and Dubey-Mallick. I will discuss some recent work with Rydh that allows us to classify subcategories in the equivariant setting and, more generally, for stacks. Non UBC Unreviewed Author affiliation: The Australian National University Postdoctoral http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
A Model of Cell Surface Receptor Aggregation
Banff International Research Station for Mathematical Innovation and Discovery
Iron, David — Unreviewed Author affiliation: Dalhousie Faculty Non UBC In this talk I will construct and analyze a model of cell receptor aggregation. We study the impact of density dependent diffusion on aggregate formation in a one-dimensional domain. Critical values of receptor diffusion and receptor activation are found and compared with numerical simulations. In the case of receptor activation the analytical results agree very well with the numerical calculations. Finally, we consider our model in higher dimensional domains. In this case our analysis is primarily numerical. http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
On Selmer groups and factoring \(p\)-adic \(L\)-functions
Banff International Research Station for Mathematical Innovation and Discovery
Palvannan, Bharathwaj — Haruzo Hida has constructed a 3-variable Rankin Helberg \(p\)-adic \(L\)-function. Two of its variables are "weight" variables and one of its variables is the "cyclotomic" variable. Samit Dasgupta has factored a certain restriction of this 3-variable \(p\)-adic \(L\)-function (when the two weight variables are set equal to each other) into a product of a 2-variable \(p\)-adic \(L\)-function (related to the adjoint representation of a Hida family) and the Kubota-Leopoldt \(p\)-adic \(L\)-function. We prove the corresponding result involving Selmer groups that is predicted by the main conjectures. A key technical input is studying the (height one) specialization of Selmer groups. Non UBC Unreviewed Graduate Author affiliation: University of Washington - Seattle http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
On the anticyclotomic main conjectures for modular forms
Banff International Research Station for Mathematical Innovation and Discovery
Büyükboduk, Kazım — I will report on recent joint work with Antonio Lei on the anticyclotomic Iwasawa theory of the base change of an elliptic modular form to an imaginary quadratic field \(K\) in which the prime \(p\) splits. We treat both the definite and indefinite cases in both \(p\)-ordinary and non-\(p\)-ordinary situations. One of our main results is an equality (up to powers of \(p\)) that is predicted by the main conjectures in the definite \(p\)-ordinary set up and a \(\Lambda\)-adic Birch and Swinnerton-Dyer formula in the indefinite case. Faculty Author affiliation: Koc University of Istanbul Unreviewed Non UBC http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
Unique Low Rank Completability of partial matrices
Banff International Research Station for Mathematical Innovation and Discovery
Jordan, Tibor — Non UBC Unreviewed Author affiliation: Eotvos University, Budapest Faculty http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
Molecular Thermodynamics for Chemical Process Modeling and Simulation
Banff International Research Station for Mathematical Innovation and Discovery
Chen, Chau-Chyun — Talk: Regular Abstract: Process modeling and simulation is a key enabling technology for chemical engineers to develop and design innovative and safe chemical processes. The underlying molecular thermodynamic models provide the scientific foundation essential for all process calculations involving thermophysical properties, heat and mass transfer, chemical reactions, phase and chemical equilibria, etc. Indeed, tremendous past accomplishments and recent advances in molecular thermodynamics have served chemical engineers well and contributed to the wide acceptance of process modeling and simulation especially in oil and gas industry and petrochemical industry. A prominent recent example is the development of a novel molecular thermodynamic model for chemical absorption of CO2 with a proprietary organic amine solution and the application of the model in the development, design, and optimization of the 1st commercial scale CO2 capture unit operated by Saskpower. However, many unsolved problems remain while new challenges emerge as chemical engineers explore new opportunities and frontiers such as carbon capture and sequestration, energy storage, saline water remediation, nuclear waste disposal, etc. This talk highlights several high impact research opportunities in the pursuit of sustainable energy. Specifically, we present new advances in molecular thermodynamics in support of modeling and simulation for high salinity produced water treatment processes in oil and gas production, defense nuclear waste treatment processes, noble metal extraction from recycled electronics, asphaltene aggregation in petroleum processing, and hybrid sulfur (HyS) cycle for hydrogen production. Non UBC Unreviewed Faculty Author affiliation: Texas Tech University http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
A New Approach to Distribution Testing
Banff International Research Station for Mathematical Innovation and Discovery
Kane, Daniel — We study the problem of determining whether or not a discrete distribution has a given property from a small number of samples. We present a new technique in this field that operates by reducing many such problems in a black box way to a simple L^2 tester. We show how this new technique can recover simple proofs of several known, optimal results and how it can be extended to provide optimal solutions to a number of previously unsolved problems. Non UBC Unreviewed Author affiliation: UCSD Faculty http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
Algebraic splines and generalized Stanley-Reisner rings
Banff International Research Station for Mathematical Innovation and Discovery
Piene, Ragni — Non UBC Unreviewed Author affiliation: University of Oslo Faculty Given a simplicial complex \(\Delta\subset \mathbb R^d\), let \(C^r_k(\Delta)\) denote the vector space of piecewise polynomial functions (algebraic splines) of degree \(\le k\) and smoothness \(r\). A major problem is to determine the dimension (and construct bases) of these vector spaces. Pioneering work by Billera, Rose, Schenck, and others gave upper and lower bounds using homological methods. The ring of continuous splines \(C^0(\Delta)=C^0_k(\Delta)\) is (essentially) equal to the face ring, or Stanley--Reisner ring, of \(\Delta\) and has the property that its geometric realization describes $\Delta$. More precisely, the part of \({\rm Spec}(C^0(\Delta))$\) lying in a certain hyperplane and having nonnegative coordinates is ``equal'' to \(\Delta\). Here we shall consider the \emph{generalized Stanley--Reisner rings} \(C^r(\Delta):=\oplus_k C^r_k(\Delta)\subset C^0(\Delta)\). We present a conjectural description of \({\rm Spec}(C^r(\Delta))\) generalizing the one for \(r=0\). To illustrate the conjecture, some very simple examples will be given. http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
Geometrically continuous splines on surfaces of arbitrary topology
Banff International Research Station for Mathematical Innovation and Discovery
Villamizar, Nelly — We study the space of geometrically continuous splines, or piecewise polynomial functions, on topological surfaces. These surfaces consist of a collection of rectangular and triangular patches together with gluing data that identifies pairs of polygonal edges. A spline is said to be G1-geometrically continuous on a topological surface if they are C1-continoous functions across the edges after the composition by a transition map. In the talk we will describe the required compatibility conditions on the transition maps so that the C1-smoothness is achieved, and give a formula for a lower bound on the dimension of the G1 spline space. In particular, we will show that this lower bound gives the exact dimension of the space for a sufficiently large degree of the polynomials pieces. We will also present some examples to illustrate the construction of basis functions for splines of small degree on particular topological surfaces. *This is a joint work with Bernard Mourrain and Raimundas Vidunas. Postdoctoral Author affiliation: RICAM Austrian Academy of Sciences Unreviewed Non UBC http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
On the classification of weakly integral modular categories
Banff International Research Station for Mathematical Innovation and Discovery
Plavnik, Julia — Non UBC In this talk we will give a panorama about the state of the problem of classification of weakly integral modular categories at the moment. We will present some of the known results for low rank and for specific dimensions, like 4m and 8m, with m a square-free odd integer. We will also explain some of the techniques that we found useful to push further the classification. Unreviewed Author affiliation: Texas A&M University Postdoctoral http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
Quantum oscillations without a magnetic field
Banff International Research Station for Mathematical Innovation and Discovery
Franz, Marcel — Author affiliation: University of British Columbia Faculty Non UBC Unreviewed http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
On heteroscedastic covariate measurement error in Cox regression
Banff International Research Station for Mathematical Innovation and Discovery
Huang, Yijian — Non UBC Unreviewed Author affiliation: Emory University Faculty Many survival studies have error-contaminated covariates, which may lack a gold standard of measurement. Furthermore, the error distribution can depend on the true covariates but the dependence structure is typically difficult to quantify; heteroscedasticity is a common manifestation. In this talk, we suggest an additive measurement error model in this circumstance, and develop a functional modeling method for Cox regression when an instrumental variable is available. The estimated regression coefficients are consistent and asymptotically normal. Preliminary numerical studies, including simulations, will be provided. http://creativecommons.org/licenses/by-nc-nd/4.0/

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