BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jade Brisson (Université Laval) DTSTART;VALUE=DATE-TIME:20221102T150000Z DTEND;VALUE=DATE-TIME:20221102T153000Z DTSTAMP;VALUE=DATE-TIME:20230926T000410Z UID:QARF/1 DESCRIPTION:Title: Loo king for eigenvalues\nby Jade Brisson (Université Laval) as part of Q uebec Analysis and Related Fields Graduate Seminar\n\n\nAbstract\nIn this talk\, you will be introduced to spectral geometry. We will briefly talk a bout what it is before focusing on one of the problem that is studied in t his field: the Steklov problem. After a historic review of this problem\, we will focus on the following question: Can we calculate its eigenvalues? \n LOCATION:https://researchseminars.org/talk/QARF/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcu-Antone Orsoni (University of Toronto) DTSTART;VALUE=DATE-TIME:20221116T160000Z DTEND;VALUE=DATE-TIME:20221116T163000Z DTSTAMP;VALUE=DATE-TIME:20230926T000410Z UID:QARF/2 DESCRIPTION:Title: Sep aration of singularities for the Bergman space and reachable space of the heat equation\nby Marcu-Antone Orsoni (University of Toronto) as part of Quebec Analysis and Related Fields Graduate Seminar\n\n\nAbstract\nLet $\\Omega_1$ and $\\Omega_2$ be two open sets of the complex plane with non empty intersection. The separation of singularities problem can be stated as follows: if $f$ belongs to the Bergman space of $\\Omega_1 \\cap \\Ome ga_2$\, can we find $f_1$ and $f_2$ belonging respectively to the Bergman spaces of $\\Omega_1$ and $\\Omega_2$\, such that $f= f_1 + f_2$? \nIn thi s talk\, we will see general settings in which the previous question has a positive answer and we will apply these results to the description of the reachable space of the heat equation. Joint work with Andreas Hartmann.\n LOCATION:https://researchseminars.org/talk/QARF/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Reihaneh Vafadar (Université Laval) DTSTART;VALUE=DATE-TIME:20221130T160000Z DTEND;VALUE=DATE-TIME:20221130T163000Z DTSTAMP;VALUE=DATE-TIME:20230926T000410Z UID:QARF/3 DESCRIPTION:Title: On divergence-free (form-bounded type) drifts\nby Reihaneh Vafadar (Unive rsité Laval) as part of Quebec Analysis and Related Fields Graduate Semin ar\n\n\nAbstract\nWe develop regularity theory for elliptic Kolmogorov ope rator with divergence-free drift in a large class (or\, more generally\, d rift having singular divergence). A key step in our proofs is "Caccioppoli 's iterations"\, used in addition to the classical De Giorgi's iterations and Moser's method.\n\nThis talk is based on joint work with Damir Kinzebu latov (Université Laval)\n LOCATION:https://researchseminars.org/talk/QARF/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Billel Guelmame (ENS de Lyon) DTSTART;VALUE=DATE-TIME:20221214T160000Z DTEND;VALUE=DATE-TIME:20221214T163000Z DTSTAMP;VALUE=DATE-TIME:20230926T000410Z UID:QARF/4 DESCRIPTION:Title: On some regularized nonlinear hyperbolic equations\nby Billel Guelmame (E NS de Lyon) as part of Quebec Analysis and Related Fields Graduate Seminar \n\n\nAbstract\nIt is known that the solutions of nonlinear hyperbolic par tial differential equations develop discontinuous shocks in finite time ev en with smooth initial data. Those shock are problematic in the theoretica l study and in the numerical computations. To avoid these shocks\, many re gularizations have been studied in the literature. For example\, adding di ffusion and/or dispersion to the equation. In this talk\, we present and s tudy some non-diffusive and non-dispersive regularizations of the Burgers equation and the barotropic Euler equations that have similar properties a s the classical equations.\n LOCATION:https://researchseminars.org/talk/QARF/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Tendron (University of Oxford) DTSTART;VALUE=DATE-TIME:20230126T160000Z DTEND;VALUE=DATE-TIME:20230126T164000Z DTSTAMP;VALUE=DATE-TIME:20230926T000410Z UID:QARF/5 DESCRIPTION:Title: A c entral limit theorem for a spatial logistic branching process in the slow coalescence regime\nby Thomas Tendron (University of Oxford) as part o f Quebec Analysis and Related Fields Graduate Seminar\n\n\nAbstract\nWe st udy the scaling limits of a spatial population dynamics model which descri bes the sizes of colonies located on the integer lattice\, and allows for branching\, coalescence in the form of local pairwise competition\, and mi gration. When started near the local equilibrium\, the rates of branching and coalescence in the particle system are both linear in the local popula tion size - we say that the coalescence is slow. We identify a rescaling o f the equilibrium fluctuations process under which it converges to an infi nite dimensional Ornstein-Uhlenbeck process with alpha-stable driving nois e if the offspring distribution lies in the domain of attraction of an alp ha-stable law with alpha between one and two.\n LOCATION:https://researchseminars.org/talk/QARF/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Mahishanka Withanachchi (Université Laval) DTSTART;VALUE=DATE-TIME:20230209T160000Z DTEND;VALUE=DATE-TIME:20230209T164000Z DTSTAMP;VALUE=DATE-TIME:20230926T000410Z UID:QARF/6 DESCRIPTION:Title: Pol ynomial approximation in local Dirichlet spaces\nby Mahishanka Withana chchi (Université Laval) as part of Quebec Analysis and Related Fields Gr aduate Seminar\n\n\nAbstract\nThe partial Taylor sums $S_n$\, $n \\geq 0$\ , are finite rank operators on any Banach space of analytic functions on t he open unit disc. In the classical setting of disc algebra\, the precise value of the norm of $S_n$ is not known and thus in the literature they ar e referred as the Lebesgue constants. In this setting\, we just know that they grow like $\\log n$\, modulo a multiplicative constant\, as $n$ tends to infinity. However\, on the weighted Dirichlet spaces $\\D_w$\, we prec isely evaluate the norm of $S_n$. As a matter of fact\, there are differen t ways to put a norm on $\\D_w$. Even though these norms are equivalent\, they lead to different values for the norm of $S_n$\, as an operator on $\ \D_w$. We present three different norms on $\\D_w$\, and in each case we try to obtain the precise value of the operator norm of $S_n$. These resul ts are in sharp contrast to the classical setting of the disc algebra. We also consider the problem for the cesaro means $\\sigma_n$ on local Dirich let spaces and try to find the norm of $\\sigma_n$ precisely for the three different norms that we introduced.\n LOCATION:https://researchseminars.org/talk/QARF/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Alain Didier Noutchegueme (Université de Montréal) DTSTART;VALUE=DATE-TIME:20230223T160000Z DTEND;VALUE=DATE-TIME:20230223T164000Z DTSTAMP;VALUE=DATE-TIME:20230926T000410Z UID:QARF/7 DESCRIPTION:Title: On minimal Surface and eigenvalues isoperimetric inequalities.\nby Alain Didier Noutchegueme (Université de Montréal) as part of Quebec Analysis and Related Fields Graduate Seminar\n\n\nAbstract\nIn the same way that ge odesics are critical curves for the length fonctional in a Riemanniann Man ifold\, Minimal Surfaces are critical hypersurfaces for the area functiona l. \n\nIn 1996\, a passionating connection have been made between Minimal Surfaces in low dimensional spheres\, and extremal riemannian metrics for eigenvalues of the Laplace-Beltrami operator on Compact Riemannian Surface s. The aim of this talk is to present such a connection\, and some more re cent extensions to more general eigenvalues problems.\n LOCATION:https://researchseminars.org/talk/QARF/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Olivier Parisé (University of Hawaii at Manoa) DTSTART;VALUE=DATE-TIME:20230406T150000Z DTEND;VALUE=DATE-TIME:20230406T154000Z DTSTAMP;VALUE=DATE-TIME:20230926T000410Z UID:QARF/8 DESCRIPTION:Title: Inv olutions of multicomplex numbers\nby Pierre-Olivier Parisé (Universit y of Hawaii at Manoa) as part of Quebec Analysis and Related Fields Gradua te Seminar\n\n\nAbstract\nGiven a real algebra $A$\, a function $f : A \\t o A$ is called a (real)-linear involution if $f$ is (real)-linear and $f(f (a)) = a$ for any element $a \\in A$. A natural question\, at least when $\\dim A < \\infty$\, is: How many (real)-linear involutions are there for a given complex algebra? \n\nWe will answer this question in the first par t of the talk for the commutative real algebra $\\mathbb{M}\\mathbb{C}(n) (n \\geq 1)$ of multicomplex numbers\, a commutative generalization of the complex numbers. In the second part of the talk\, I will show how to defi ne different Laplacians using the (real)-linear involutions of the multico mplex numbers.\n\nThe first part of this talk is a joint work with Nicolas Doyon and William Verreault.\n LOCATION:https://researchseminars.org/talk/QARF/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Antoine Metras (University of Bristol) DTSTART;VALUE=DATE-TIME:20230309T160000Z DTEND;VALUE=DATE-TIME:20230309T164000Z DTSTAMP;VALUE=DATE-TIME:20230926T000410Z UID:QARF/9 DESCRIPTION:Title: Eig envalue optimisation and n-harmonic maps\nby Antoine Metras (Universit y of Bristol) as part of Quebec Analysis and Related Fields Graduate Semin ar\n\n\nAbstract\nOn a surface\, eigenvalue optimisation with respect to t he metric leads to minimal surfaces (in a sphere for Laplace eigenvalue\, free boundary minimal in a ball for Steklov ones). When we restrict the op timisation problem to a conformal class\, the corresponding object we obta in are harmonic maps. I will discuss generalisation to higher dimension of these results and how n-harmonic maps play a crucial role in it.\n LOCATION:https://researchseminars.org/talk/QARF/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuveshen Mooroogen (University of British Columbia) DTSTART;VALUE=DATE-TIME:20230420T150000Z DTEND;VALUE=DATE-TIME:20230420T154000Z DTSTAMP;VALUE=DATE-TIME:20230926T000410Z UID:QARF/10 DESCRIPTION:Title: La rge subsets of Euclidean space avoiding infinite arithmetic progressions\nby Yuveshen Mooroogen (University of British Columbia) as part of Queb ec Analysis and Related Fields Graduate Seminar\n\n\nAbstract\nAn arithmet ic progression (AP) is a collection of equally-spaced real numbers. It may be finite or countably infinite. It is known that if a subset of the real line has positive Lebesgue measure\, then it contains a k-term AP for eve ry natural number k. In joint work with Laurestine Bradford (McGill\, Ling uistics) and Hannah Kohut (UBC\, Mathematics)\, we prove that this result does not extend to infinite APs in the following sense: for each real numb er p in [0\,1)\, we construct a subset of the real line that intersects ev ery interval of unit length in a set of measure at least p\, but that does not contain any infinite AP. In this presentation\, I will explain the ge ometric features of our set that allow it to avoid such progressions. I wi ll also briefly discuss two recent preprints\, due to Kolountzakis-Papageo rgiou and Burgin-Goldberg-Keleti-MacMahon-Wang\, that were inspired by our work. These respectively employ probabilistic and topological methods\, i n contrast to our argument\, which relies on measure theory and equidistri bution of sequences mod 1.\n LOCATION:https://researchseminars.org/talk/QARF/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Frantz (Université de Lorraine) DTSTART;VALUE=DATE-TIME:20230504T150000Z DTEND;VALUE=DATE-TIME:20230504T154000Z DTSTAMP;VALUE=DATE-TIME:20230926T000410Z UID:QARF/11 DESCRIPTION:Title: In troduction to scattering theory on Hilbert spaces.\nby Nicolas Frantz (Université de Lorraine) as part of Quebec Analysis and Related Fields Gr aduate Seminar\n\n\nAbstract\nThe goal of scattering theory is to write th e asymptotic of solutions of Schrödinger equation associated to a complex Hamiltonian in term of solutions of Schrödinger equation associated to a simpler Hamiltonian. \nAfter describing how theory of Hilbert space can d escribe quantum system\, I will introduce the main ideas of scattering the ory for self-adjoint operator. If I have enough time\, I will explain how to extend this theory to non-self-adjoint Hamiltonian.\n LOCATION:https://researchseminars.org/talk/QARF/11/ END:VEVENT END:VCALENDAR