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BEGIN:VEVENT
SUMMARY:Elizabeth Meckes (Case Western Reserve University)
DTSTART:20201013T143000Z
DTEND:20201013T153000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/1/">Random Matrices with Prescribed Eigenvalues</a>\nby Elizabeth Mec
 kes (Case Western Reserve University) as part of Oxford Random Matrix Theo
 ry Seminars\n\n\nAbstract\nClassical random matrix theory begins with a ra
 ndom matrix model and analyzes the distribution of the resulting eigenvalu
 es.  In this work\, we treat the reverse question: if the eigenvalues are 
 specified but the matrix is "otherwise random"\, what do the entries typic
 ally look like?  I will describe a natural model of random matrices with p
 rescribed eigenvalues and discuss a central limit theorem for projections\
 , which in particular shows that relatively large subcollections of entrie
 s are jointly Gaussian\, no matter what the eigenvalue distribution looks 
 like.  I will discuss various applications and interpretations of this res
 ult\, in particular to a probabilistic version of the Schur--Horn theorem 
 and to models of quantum systems in random states.  This work is joint wit
 h Mark Meckes.\n\nPlease subscribe to our mailing list (https://lists.math
 s.ox.ac.uk/mailman/listinfo/random-matrix-theory-announce) and Zoom link w
 ill be made available the day before.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Meckes (Case Western Reserve University)
DTSTART:20201020T143000Z
DTEND:20201020T153000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/2/">Comparing counting functions for determinantal point processes</a
 >\nby Mark Meckes (Case Western Reserve University) as part of Oxford Rand
 om Matrix Theory Seminars\n\n\nAbstract\nI will describe a general method 
 for comparing the counting functions of determinantal point processes in t
 erms of trace class norm distances between their kernels (and review what 
 all of those words mean). Then I will outline joint work with Elizabeth Me
 ckes using this method to prove a version of a self-similarity property of
  eigenvalues of Haar-distributed unitary matrices conjectured by Coram and
  Diaconis.  Finally\, I will discuss ongoing work by my PhD student Kyle T
 aljan\, bounding the rate of convergence for counting functions of GUE eig
 envalues to the Sine or Airy process counting functions.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antti Knowles (Université de Genève)
DTSTART:20201027T153000Z
DTEND:20201027T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/4/">Delocalization transition for critical Erdös-Rényi graphs</a>\n
 by Antti Knowles (Université de Genève) as part of Oxford Random Matrix 
 Theory Seminars\n\n\nAbstract\nWe analyse the eigenvectors of the adjacenc
 y matrix of a critical Erdös-Rényi graph G(N\,d/N)\, where d is of order
  \\log N. We show that its spectrum splits into two phases: a delocalized 
 phase in the middle of the spectrum\, where the eigenvectors are completel
 y delocalized\, and a semilocalized phase near the edges of the spectrum\,
  where the eigenvectors are essentially localized on a small number of ver
 tices. In the semilocalized phase the mass of an eigenvector is concentrat
 ed in a small number of disjoint balls centred around resonant vertices\, 
 in each of which it is a radial exponentially decaying function. The trans
 ition between the phases is sharp and is manifested in a discontinuity in 
 the localization exponents of the eigenvectors. Joint work with Johannes A
 lt and Raphael Ducatez.\n\nThis seminar will be held via zoom. Meeting lin
 k will be sent to members of our mailing list (https://lists.maths.ox.ac.u
 k/mailman/listinfo/random-matrix-theory-announce) in our weekly announceme
 nt on Monday.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bothner (University of Bristol)
DTSTART:20201103T153000Z
DTEND:20201103T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/5/">A threefold way to integrable probabilistic models</a>\nby Thomas
  Bothner (University of Bristol) as part of Oxford Random Matrix Theory Se
 minars\n\n\nAbstract\nThis talk is intended for a broad math and physics a
 udience in particular including students. It will focus on the speaker's r
 ecent contributions to the analysis of the real Ginibre ensemble consistin
 g of square real matrices whose entries are i.i.d. standard normal random 
 variables. In sharp contrast to the complex and quaternion Ginibre ensembl
 e\, real eigenvalues in the real Ginibre ensemble attain positive likeliho
 od. In turn\, the spectral radius of a real Ginibre matrix follows a diffe
 rent limiting law for purely real eigenvalues than for non-real ones. We w
 ill show that the limiting distribution of the largest real eigenvalue adm
 its a closed form expression in terms of a distinguished solution to an in
 verse scattering problem for the Zakharov-Shabat system. This system is di
 rectly related to several of the most interesting nonlinear evolution equa
 tions in $1+1$ dimensions which are solvable by the inverse scattering met
 hod. The results of this talk are based on our joint work with Jinho Baik 
 (arXiv:1808.02419 and arXiv:2008.01694).\n\nThis seminar will be held via 
 zoom. Meeting link will be sent to members of our mailing list (https://li
 sts.maths.ox.ac.uk/mailman/listinfo/random-matrix-theory-announce) in our 
 weekly announcement on Monday.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Assiotis (University of Edinburgh)
DTSTART:20201110T153000Z
DTEND:20201110T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/6/">On the joint moments of characteristic polynomials of random unit
 ary matrices</a>\nby Theo Assiotis (University of Edinburgh) as part of Ox
 ford Random Matrix Theory Seminars\n\n\nAbstract\nI will talk about the jo
 int moments of characteristic polynomials of random unitary matrices and t
 heir derivatives. In joint work with Jon Keating and Jon Warren we establi
 sh the asymptotics of these quantities for general real values of the expo
 nents as the size N of the matrix goes to infinity. This proves a conjectu
 re of Hughes from 2001. In subsequent joint work with Benjamin Bedert\, Mu
 stafa Alper Gunes and Arun Soor we focus on the leading order coefficient 
 in the asymptotics\, we connect this to Painleve equations for general val
 ues of the exponents and obtain explicit expressions corresponding to the 
 so-called classical solutions of these equations.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nina Snaith (University of Bristol)
DTSTART:20201117T153000Z
DTEND:20201117T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/7/">Zeros\, moments and derivatives</a>\nby Nina Snaith (University o
 f Bristol) as part of Oxford Random Matrix Theory Seminars\n\n\nAbstract\n
 For 20 years we have known that average values of characteristic polynomia
 ls of random unitary matrices provide a good model for moments of the Riem
 ann zeta function.  Now we consider moments of the logarithmic derivative 
 of characteristic polynomials\, calculations which are motivated by questi
 ons on the distribution of zeros of the derivative of the Riemann zeta fun
 ction.  Joint work with Emilia Alvarez.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Claeys (Universite catholique de louvain)
DTSTART:20201124T153000Z
DTEND:20201124T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/8/">Asymptotics for averages over classical orthogonal ensembles</a>\
 nby Tom Claeys (Universite catholique de louvain) as part of Oxford Random
  Matrix Theory Seminars\n\n\nAbstract\nAverages of multiplicative eigenval
 ue statistics of Haar distributed unitary matrices are Toeplitz determinan
 ts\, and asymptotics for these determinants are now well understood for la
 rge classes of symbols\, including symbols with gaps and (merging) Fisher-
 Hartwig singularities. Similar averages for Haar distributed orthogonal ma
 trices are Toeplitz+Hankel determinants. Some asymptotic results for these
  determinants are known\, but not in the same generality as for Toeplitz d
 eterminants. I will explain how one can systematically deduce asymptotics 
 for averages in the orthogonal group from those in the unitary group\, usi
 ng a transformation formula and asymptotics for certain orthogonal polynom
 ials on the unit circle\, and I will show that this procedure leads to asy
 mptotic results for symbols with gaps or (merging) Fisher-Hartwig singular
 ities. The talk will be based on joint work with Gabriel Glesner\, Alexand
 er Minakov and Meng Yang.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Hartung (Johannes Gutenberg University Mainz)
DTSTART:20201201T153000Z
DTEND:20201201T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/9/">Maxima of a random model of the Riemann zeta function on longer i
 ntervals (and branching random walks)</a>\nby Lisa Hartung (Johannes Guten
 berg University Mainz) as part of Oxford Random Matrix Theory Seminars\n\n
 \nAbstract\nWe study the maximum of a random model for the Riemann zeta fu
 nction (on the critical line  at height T) on the interval $[−(\\log T)^
 \\theta\,(\\log T)^\\theta)$\, where $\\theta=(\\log\\log T)−a$\, with $
 0 < a < 1$.  We obtain the leading order as well as the logarithmic correc
 tion of the maximum. \n\nAs it turns out a good toy model is a collection 
 of independent BRW’s\, where the number of independent copies depends on
  θ. In this talk I will try to motivate our results by mainly focusing on
  this toy model. The talk is based on joint work in progress with L.-P. Ar
 guin and G. Dubach.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatyana Shcherbina (University of Wisconsin-Madison)
DTSTART:20210119T153000Z
DTEND:20210119T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/10
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/10/">Universality for random band matrices</a>\nby Tatyana Shcherbina
  (University of Wisconsin-Madison) as part of Oxford Random Matrix Theory 
 Seminars\n\n\nAbstract\nRandom band matrices (RBM) are natural intermediat
 e models to study eigenvalue statistics and quantum propagation in disorde
 red systems\, since they interpolate between mean-field type Wigner matric
 es and random Schrodinger operators. In particular\, RBM can be used to mo
 del the Anderson metal-insulator phase transition (crossover) even in 1d. 
 In this talk we will discuss some recent progress in application of the su
 persymmetric method (SUSY) and transfer matrix approach to the analysis of
  local spectral characteristics of some specific types of 1d RBM.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Najnudel (University of Bristol)
DTSTART:20210126T153000Z
DTEND:20210126T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/11/">Secular coefficients and the holomorphic multiplicative chaos</a
 >\nby Joseph Najnudel (University of Bristol) as part of Oxford Random Mat
 rix Theory Seminars\n\n\nAbstract\nWe study the coefficients of the charac
 teristic polynomial (also called secular coefficients) of random unitary m
 atrices drawn from the Circular Beta Ensemble (i.e. the joint probability 
 density of the eigenvalues is proportional to the product of the power bet
 a of the mutual distances between the points). We study the behavior of th
 e secular coefficients when the degree of the coefficient and the dimensio
 n of the matrix tend to infinity. The order of magnitude of this coefficie
 nt depends on the value of the parameter beta\, in particular\, for beta =
  2\, we show that the middle coefficient of the characteristic polynomial 
 of the Circular Unitary Ensemble converges to zero in probability when the
  dimension goes to infinity\, which solves an open problem of Diaconis and
  Gamburd. We also find a limiting distribution for some renormalized coeff
 icients in the case where beta > 4. In order to prove our results\, we int
 roduce a holomorphic version of the Gaussian Multiplicative Chaos\, and we
  also make a connection with random permutations following the Ewens measu
 re.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Życzkowski (Jagiellonian University)
DTSTART:20210202T153000Z
DTEND:20210202T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/12
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/12/">Universal spectra of random channels and random Lindblad operato
 rs</a>\nby Karol Życzkowski (Jagiellonian University) as part of Oxford R
 andom Matrix Theory Seminars\n\n\nAbstract\nWe analyze spectral properties
  of generic quantum operations\, which describe open systems under assumpt
 ion of a strong decoherence and a strong coupling with an environment. In 
 the case of discrete maps the spectrum of a quantum stochastic map display
 s a universal behaviour: it contains the leading eigenvalue $\\lambda_1 = 
 1$\, while all other eigenvalues are restricted to the disk of radius $R<1
 $. Similar properties are exhibited by spectra of their classical counterp
 arts - random stochastic matrices. In the case of a generic dynamics in co
 ntinuous time\, we introduce an ensemble of random Lindblad operators\, wh
 ich generate Markov evolution in the space of density matrices of a fixed 
 size. Universal spectral features of such operators\, including the lemon-
 like shape of the spectrum in the complex plane\, are explained with a non
 -hermitian random matrix model. The structure of the spectrum determines t
 he transient behaviour of the quantum system and the convergence of the dy
 namics towards the generically unique invariant state. The quantum-to-clas
 sical transition for this model is also studied and the spectra of random 
 Kolmogorov operators are investigated.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Nahum (University of Oxford)
DTSTART:20210209T153000Z
DTEND:20210209T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/13
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/13/">Random quantum circuits and many-body dynamics</a>\nby Adam Nahu
 m (University of Oxford) as part of Oxford Random Matrix Theory Seminars\n
 \n\nAbstract\nA quantum circuit defines a discrete-time evolution for a se
 t of quantum spins/qubits\, via a sequence of unitary 'gates’ coupling n
 earby spins. I will describe how random quantum circuits\, where each gate
  is a random unitary matrix\, serve as minimal models for various universa
 l features of many-body dynamics. These include the dynamical generation o
 f entanglement between distant spatial regions\, and the quantum "butterfl
 y effect". I will give a very schematic overview of mappings that relate a
 verages in random circuits to the classical statistical mechanics of rando
 m paths. Time permitting\, I will describe a new phase transition in the d
 ynamics of a many-body wavefunction\, due to repeated measurements by an e
 xternal observer.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Moran (University of Oxford)
DTSTART:20210216T153000Z
DTEND:20210216T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/14
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/14/">Critically stable network economies</a>\nby Jose Moran (Universi
 ty of Oxford) as part of Oxford Random Matrix Theory Seminars\n\n\nAbstrac
 t\nWill a large economy be stable? In this talk\, I will present a model f
 or a network economy where firms' productions are interdependent\, and stu
 dy the conditions under which such input-output networks admit a competiti
 ve economic equilibrium\, where markets clear and profits are zero. Insigh
 ts from random matrix theory allow to understand some of the emergent prop
 erties of this equilibrium and to provide a classification for the differe
 nt types of crises it can be subject to. After this\, I will endow the mod
 el with dynamics\, and present results with strong links to generalised Lo
 tka-Volterra models in theoretical ecology\, where inter-species interacti
 ons are modelled with random matrices and where the system naturally self-
 organises into a critical state. In both cases\, the stationary points mus
 t consist of positive species populations/prices/outputs. Building on thes
 e ideas\, I will show the key concepts behind an economic agent-based mode
 l that can exhibit convergence to equilibrium\, limit cycles and chaotic d
 ynamics\, as well as a phase of spontaneous crises whose origin can be und
 erstood using "semi-linear" dynamics.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yacine Barhoumi (Ruhr-Universität Bochum)
DTSTART:20210223T153000Z
DTEND:20210223T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/15
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/15/">A new approach to the characteristic polynomial of a random unit
 ary matrix</a>\nby Yacine Barhoumi (Ruhr-Universität Bochum) as part of O
 xford Random Matrix Theory Seminars\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diane Holcomb (KTH Stockholm)
DTSTART:20210302T153000Z
DTEND:20210302T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/16
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/16/">The stochastic Airy operator and an interesting eigenvalue proce
 ss</a>\nby Diane Holcomb (KTH Stockholm) as part of Oxford Random Matrix T
 heory Seminars\n\n\nAbstract\nThe Gaussian ensembles\, originally introduc
 ed by Wigner may be generalized to an n-point ensemble called the beta-Her
 mite ensemble. As with the original ensembles we are interested in studyin
 g the local behavior of the eigenvalues. At the edges of the ensemble the 
 rescaled eigenvalues converge to the Airy_beta process which for general b
 eta is characterized as the eigenvalues of a certain random differential o
 perator called the stochastic Airy operator (SAO). In this talk I will giv
 e a short introduction to the Stochastic Airy Operator and the proof of co
 nvergence of the eigenvalues\, before introducing another interesting eige
 nvalue process. This process can be characterized as a limit of eigenvalue
 s of minors of the tridiagonal matrix model associated to the beta-Hermite
  ensemble as well as the process formed by the eigenvalues of the SAO unde
 r a restriction of the domain. This is joint work with Angelica Gonzalez.\
 n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gernot Akemann (Universität Bielefeld)
DTSTART:20210309T153000Z
DTEND:20210309T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/17
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/17/">Territorial behaviour of buzzards and the 2D Coulomb gas</a>\nby
  Gernot Akemann (Universität Bielefeld) as part of Oxford Random Matrix T
 heory Seminars\n\n\nAbstract\nNon-Hermitian random matrices with complex e
 igenvalues represent a truly two-dimensional (2D) Coulomb gas at inverse t
 emperature beta=2. Compared to their Hermitian counter-parts they enjoy an
  enlarged bulk and edge universality. As an application to ecology we mode
 l large scale data of the approximately 2D distribution of buzzard nests i
 n the Teutoburger forest observed over a period of 20 y. These birds of pr
 ey show a highly territorial behaviour. Their occupied nests are monitored
  annually and we compare these data with a one-component 2D Coulomb gas of
  repelling charges as a function of beta. The nearest neighbour spacing di
 stribution of the nests is well described by fitting to beta as an effecti
 ve repulsion parameter\, that lies between the universal predictions of Po
 isson (beta=0) and random matrix statistics (beta=2). Using a time moving 
 average and comparing with next-to-nearest neighbours we examine the effec
 t of a population increase on beta and correlation length.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arno Kuijlaars (KU Leuven)
DTSTART:20210427T143000Z
DTEND:20210427T153000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/18
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/18/">The two-periodic Aztec diamond and matrix valued orthogonality</
 a>\nby Arno Kuijlaars (KU Leuven) as part of Oxford Random Matrix Theory S
 eminars\n\n\nAbstract\nI will discuss how polynomials with a non-hermitian
  orthogonality on a contour in the complex plane arise in certain random t
 iling problems. In the case of periodic weightings the orthogonality is ma
 trixvalued.\n\nIn work with Maurice Duits (KTH Stockholm) the Riemann-Hilb
 ert problem for matrix valued orthogonal polynomials was used to obtain as
 ymptotics for domino tilings of the two-periodic Aztec diamond. This model
  is remarkable since it gives rise to a gaseous phase\, in addition to the
  more common solid and liquid phases.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liza Rebrova (Lawrence Berkeley National Lab)
DTSTART:20210504T143000Z
DTEND:20210504T153000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/19
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/19/">On the iterative methods for corrupted linear systems</a>\nby Li
 za Rebrova (Lawrence Berkeley National Lab) as part of Oxford Random Matri
 x Theory Seminars\n\n\nAbstract\nA group of projection based approaches fo
 r solving large-scale linear systems is known for its speed and simplicity
 . For example\, Kaczmarz algorithm iteratively projects the previous appro
 ximation x_k onto the solution spaces of the next equation in the system. 
 An elegant proof of the exponential convergence of this method\, using cor
 rect randomization of the process\, was given in 2009 by Strohmer and Vers
 hynin\, and succeeded by many extensions and generalizations. I will discu
 ss our newly developed variants of these methods that successfully avoid l
 arge and potentially adversarial corruptions in the linear system. I speci
 fically focus on the random matrix and high-dimensional probability result
 s that play a crucial role in proving convergence of such methods. Based o
 n the joint work with Jamie Haddock\, Deanna Needell\, and Will Swartworth
 .\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Khoruzhenko (Queen Mary University London)
DTSTART:20210511T143000Z
DTEND:20210511T153000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/20
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/20/">How many stable equilibria will a large complex system have?</a>
 \nby Boris Khoruzhenko (Queen Mary University London) as part of Oxford Ra
 ndom Matrix Theory Seminars\n\n\nAbstract\nIn 1972 Robert May argued that 
 (generic) complex systems become unstable to small displacements from equi
 libria as the system complexity increases. His analytical model and outloo
 k was linear. I will talk about a “minimal” non-linear extension of Ma
 y’s model – a nonlinear autonomous system of N ≫ 1 degrees of freedo
 m randomly coupled by both relaxational (’gradient’) and non-relaxatio
 nal (’solenoidal’) random interactions. With the increasing interactio
 n strength such systems undergo an abrupt transition from a trivial phase 
 portrait with a single stable equilibrium into a topologically non-trivial
  regime where equilibria are on average exponentially abundant\, but typic
 ally all of them are unstable\, unless the dynamics is purely gradient. Wh
 en the interaction strength increases even further the stable equilibria e
 ventually become on average exponentially abundant unless the interaction 
 is purely solenoidal. One can investigate these transitions with the help 
 of the Kac-Rice formula for counting zeros of random functions and theory 
 of random matrices applied to the real elliptic ensemble with some of the 
 mathematical problems remaining open. This talk is based on collaborative 
 work with Gerard Ben Arous and Yan Fyodorov.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maurice Duits (KTH Stockholm)
DTSTART:20210518T143000Z
DTEND:20210518T153000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/21
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/21/">Integrability of random tilings with doubly periodic weights</a>
 \nby Maurice Duits (KTH Stockholm) as part of Oxford Random Matrix Theory 
 Seminars\n\n\nAbstract\nIn recent years important progress has been made i
 n the understanding of random tilings of large Aztec diamonds with doubly 
 periodic weights. Due to the double periodicity a new phase appears that  
 has not been observed in tiling models with uniform weights. One of the ch
 allenges is to find expressions of for the correlation functions that are 
 amenable for asymptotic studies. In the case of the uniform weight the mod
 el is an example of a Schur process and\, consequently\,  such expressions
  for the correlation functions are known and well-studied in that case. In
  a joint work with Tomas Berggren we studied a more  general  integrable s
 tructure that includes certain doubly periodic weightings planar domains\,
  such as the Aztec diamond.  A key feature is a dynamical system hiding in
  the background. In case of a periodic orbit\, explicit double integrals f
 or the correlation function can be found\, paving the way for an asymptoti
 c study using saddle point methods.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mo Dick Wong (University of Oxford)
DTSTART:20210525T143000Z
DTEND:20210525T153000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/22
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/22/">There has been a lot of interest in recent years in understandin
 g the multifractality of characteristic polynomials of random matrices. In
  this talk I shall consider the study of moments of moments from the proba
 bilistic perspective of Gaussian multiplicat</a>\nby Mo Dick Wong (Univers
 ity of Oxford) as part of Oxford Random Matrix Theory Seminars\n\n\nAbstra
 ct\nThere has been a lot of interest in recent years in understanding the 
 multifractality of characteristic polynomials of random matrices. In this 
 talk I shall consider the study of moments of moments from the probabilist
 ic perspective of Gaussian multiplicative chaos\, and in particular establ
 ish exact asymptotics for the so-called critical-subcritical regime in the
  context of large Haar-distributed unitary matrices. This is based on a jo
 int work with Jon Keating.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Tikhomirov (Georgia Institute of Technology)
DTSTART:20210601T130000Z
DTEND:20210601T140000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/23
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/23/">Invertibility of random square matrices</a>\nby Konstantin Tikho
 mirov (Georgia Institute of Technology) as part of Oxford Random Matrix Th
 eory Seminars\n\n\nAbstract\nConsider an n by n random matrix A with i.i.d
  entries. In this talk\, we discuss some results on the magnitude of the s
 mallest singular value of A\, and\, in particular\, the problem of estimat
 ing the singularity probability when the entries of A are discrete.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Pitchford (University of York)
DTSTART:20210615T143000Z
DTEND:20210615T153000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/24
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/24/">Are random matrix models useful in biological systems?</a>\nby J
 on Pitchford (University of York) as part of Oxford Random Matrix Theory S
 eminars\n\n\nAbstract\nFor five decades\, mathematicians have exploited th
 e beauties of random matrix theory (RMT) in the hope of discovering princi
 ples which govern complex ecosystems. While RMT lies at the heart of the i
 deas\, their translation toward biological reality requires some heavy lif
 ting: dynamical systems theory\, statistics\, and large-scale computations
  are involved\, and any predictions should be challenged with empirical da
 ta. This can become very awkward.\n\nIn addition to a morose journey throu
 gh some of my personal failures to make RMT meet reality\, I will try to s
 ketch out some more constructive future perspectives. In particular\, new 
 methods for microbial community composition\, dynamics and evolution might
  allow us to apply RMT ideas to the treatment of cystic fibrosis. In addit
 ion\, in fisheries I will argue that sometimes the very absence of an empi
 rical dataset can add to the practical value of models as tools to influen
 ce policy.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gérard Ben Arous (New York University)
DTSTART:20210601T143000Z
DTEND:20210601T153000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/25
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/25/">Random Determinants and the Elastic Manifold</a>\nby Gérard Ben
  Arous (New York University) as part of Oxford Random Matrix Theory Semina
 rs\n\n\nAbstract\nThis is joint work with Paul Bourgade and Benjamin McKen
 na (Courant Institute\, NYU).\n\nThe elastic manifold is a paradigmatic re
 presentative of the class of disordered elastic systems. These models desc
 ribe random surfaces with rugged shapes resulting from a competition betwe
 en random spatial impurities (preferring disordered configurations)\, on t
 he one hand\, and elastic self-interactions (preferring ordered configurat
 ions)\, on the other. The elastic manifold model is interesting because it
  displays a depinning phase transition and has a long history as a testing
  ground for new approaches in statistical physics of disordered media\, fo
 r example for fixed dimension by Fisher (1986) using functional renormaliz
 ation group methods\, and in the high-dimensional limit by Mézard and Pa
 risi (1992) using the replica method. \n\nWe study the topology of the ene
 rgy landscape of this model in the Mézard-Parisi setting\, and compute th
 e (annealed) topological complexity both of total critical points and of l
 ocal minima. Our main result confirms the recent formulas by Fyodorov and 
 Le Doussal (2020) and allows to identify the boundary between simple and g
 lassy phases. The core argument relies on the analysis of the asymptotic b
 ehavior of large random determinants in the exponential scale.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Edelman (MIT)
DTSTART:20210610T130000Z
DTEND:20210610T140000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/26
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/26/">53 Matrix Factorizations\, generalized Cartan\, and Random Matri
 x Theory</a>\nby Alan Edelman (MIT) as part of Oxford Random Matrix Theory
  Seminars\n\n\nAbstract\nAn insightful exercise might be to ask what is th
 e most important idea in linear algebra. Our first answer would not be eig
 envalues or linearity\, it would be “matrix factorizations.”  We will 
 discuss a blueprint to generate  53 inter-related matrix factorizations (t
 imes 2) most of which appear to be new. The underlying mathematics may be 
 traced back to Cartan (1927)\, Harish-Chandra (1956)\, and Flensted-Jensen
  (1978) . We will discuss the interesting history. One anecdote is that Eu
 gene Wigner (1968) discovered factorizations such as the svd in passing in
  a way that was buried and only eight authors have referenced that work. I
 ronically Wigner referenced Sigurður Helgason (1962) but Wigner did not r
 ecognize his results in Helgason's book. This work also extends upon and c
 ompletes open problems posed by Mackey²&Tisseur (2003/2005).\n\nClassical
  results of Random Matrix Theory concern exact formulas from the Hermite\,
  Laguerre\, Jacobi\, and Circular distributions. Following an insight from
  Freeman Dyson (1970)\, Zirnbauer (1996) and Duenez (2004/5) linked some o
 f these classical ensembles to Cartan's theory of Symmetric Spaces. One tr
 oubling fact is that symmetric spaces alone do not cover all of the Jacobi
  ensembles. We present a completed theory based on the generalized Cartan 
 distribution. Furthermore\, we show how the matrix factorization obtained 
 by the generalized Cartan decomposition G=K₁AK₂ plays a crucial role i
 n sampling algorithms and the derivation of the joint probability density 
 of A.\n\nJoint work with Sungwoo Jeong.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Florea (UCI)
DTSTART:20211130T153000Z
DTEND:20211130T163000Z
DTSTAMP:20260404T095827Z
UID:OxfordRMT/27
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Oxfor
 dRMT/27/">The Ratios Conjecture over function fields</a>\nby Alexandra Flo
 rea (UCI) as part of Oxford Random Matrix Theory Seminars\n\n\nAbstract\nI
  will talk about some recent joint work with H. Bui and J. Keating where w
 e study the Ratios Conjecture for the family of quadratic L-functions over
  function fields. I will also discuss the closely related problem of obtai
 ning upper bounds for negative moments of L-functions\, which allows us to
  obtain partial results towards the Ratios Conjecture in the case of one o
 ver one\, two over two and three over three L-functions.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordRMT/27/
END:VEVENT
END:VCALENDAR