BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Orr Shalit (Technion) DTSTART:20210802T140000Z DTEND:20210802T145000Z DTSTAMP:20260422T185352Z UID:CMO-21w5124/1 DESCRIPTION:Title: Davidson and Kennedy’s take on noncommutative convexity\nby Orr Shalit (Technion) as part of CMO workshop: Multivariable Operator Theory and Function Spaces in several Variables\n\n\nAbstract\nI will present Dav idson and Kennedy’s theory of noncommutative convexity and noncommutativ e Choquet theory\, which appeared in a preprint two years ago. I will comp are to older notions of convexity\, such as matrix convexity\, and illustr ate what it can do for us.\n LOCATION:https://researchseminars.org/talk/CMO-21w5124/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Jury (University of Florida) DTSTART:20210802T150500Z DTEND:20210802T155500Z DTSTAMP:20260422T185352Z UID:CMO-21w5124/2 DESCRIPTION:Title: Geometry of free loci and factorization of noncommutative polynomials (Helton\, Klep\, Volčič)\nby Michael Jury (University of Florida) as part of CMO workshop: Multivariable Operator Theory and Function Spaces in several Variables\n\n\nAbstract\nWe will discuss the paper of Helton\, Klep\, and Volčič with this title (and present some relevant background) . It concerns the zero locus of a noncommutative polynomial. If p is a non commutative polynomial in d variables\, its zero locus is defined to be th e set of d-tuples of square matrices X\, of all sizes\, for which det(p(X) )=0. It is proved (among other things) that p is irreducible if and only i f the zero locus (at size n) is an irreducible variety for sufficiently la rge n. A key step in the proof is an irreducibility result for linear penc ils.\n LOCATION:https://researchseminars.org/talk/CMO-21w5124/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Yi Wang (Vanderbilt University) DTSTART:20210802T161500Z DTEND:20210802T170500Z DTSTAMP:20260422T185352Z UID:CMO-21w5124/3 DESCRIPTION:Title: The Drury-Arveson space as an L2 space defined by a distribution\n by Yi Wang (Vanderbilt University) as part of CMO workshop: Multivariable Operator Theory and Function Spaces in several Variables\n\n\nAbstract\nI will try to discuss some of the basic properties of the Drury-Arveson spa ce from a different point of view: that is\, to view the Drury Arveson spa ce as an analytic function space that is $L^2$ integrable with a distribut ion. This is based on several papers by Shalit\, Arcozzi\, Rochberg\, Sawy er\, etc\n LOCATION:https://researchseminars.org/talk/CMO-21w5124/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Dor-On (University of Copenhagen) DTSTART:20210803T140000Z DTEND:20210803T145000Z DTSTAMP:20260422T185352Z UID:CMO-21w5124/4 DESCRIPTION:Title: Blaschke-Singular-Outer factorization for analytic free functions on t he nc unit ball\nby Adam Dor-On (University of Copenhagen) as part of CMO workshop: Multivariable Operator Theory and Function Spaces in severa l Variables\n\n\nAbstract\nA classical result of Herglotz and F. Riesz say s that any bounded holomorphic function on the unit disk admits a factoriz ation into a product of an inner Blaschke product\, an inner singular func tion and an outer function. We will discuss an extension of this result\, due to Jury\, Martin and Shamovich\, to free analytic functions on the non -commutative unit ball. Time permitting\, we will showcase some examples c oming from nc rational functions.\n LOCATION:https://researchseminars.org/talk/CMO-21w5124/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikolaos Chalmoukis (University of Bologna) DTSTART:20210803T150500Z DTEND:20210803T155500Z DTSTAMP:20260422T185352Z UID:CMO-21w5124/5 DESCRIPTION:Title: Hardy Sobolev spaces in several complex variables\nby Nikolaos Cha lmoukis (University of Bologna) as part of CMO workshop: Multivariable Op erator Theory and Function Spaces in several Variables\n\n\nAbstract\nThe class of Hardy Sobolev spaces in the unit ball of C^n is a family of space s including the Hardy\, Drury Arveson\, Bergman and Dirichlet space. In th is talk we will focus on questions such as characterization of multipliers \, interpolating sequences and exceptional sets\, mostly presenting earlie r work of Ahern\, Work\, Verbitsky and others. \nIn particular we find tha t a common factor of all these problems is an abstract potential theory du e to Adams and Hedberg adapted to the setting of Hardy Sobolev spaces. \nW e shall make an effort to highlight the limitations of the techniques that have been used so far and present some open problems that might be of int erest.\n LOCATION:https://researchseminars.org/talk/CMO-21w5124/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Kelly Bickel (Bucknell University) DTSTART:20210803T161500Z DTEND:20210803T170500Z DTSTAMP:20260422T185352Z UID:CMO-21w5124/6 DESCRIPTION:Title: Pascoe’s NC Free Universal Monodromy Theorem and Applications\nb y Kelly Bickel (Bucknell University) as part of CMO workshop: Multivariab le Operator Theory and Function Spaces in several Variables\n\n\nAbstract\ nA crucial assumption of the classical monodromy theorem states that the u nderlying domain must be simply connected. Recent work by J.E. Pascoe has established the surprising fact that\, in the non-commutative free setting \, “simply connected” can be replaced with merely “connected.” Thi s talk is based on Pascoe’s associated paper “Non-commutative Free Uni versal Monodromy\, Pluriharmonic Conjugates\, and Plurisubharmonicity” a nd will provide both the geometric intuition behind his monodromy theorem as well as a number of interesting applications.\n LOCATION:https://researchseminars.org/talk/CMO-21w5124/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Eli Shamovich (Ben-Gurion University) DTSTART:20210805T140000Z DTEND:20210805T145000Z DTSTAMP:20260422T185352Z UID:CMO-21w5124/7 DESCRIPTION:Title: Residual finite-dimensionality for operator algebras\nby Eli Shamo vich (Ben-Gurion University) as part of CMO workshop: Multivariable Opera tor Theory and Function Spaces in several Variables\n\n\nAbstract\nIn this talk\, I will present the works of Clouatre and Dor-On and Clouatre and R amsey. These works define and study residual finite-dimensionality for non -self-adjoint operator algebras. In particular\, we will explore the resid ual finite-dimensionality of the maximal C^*-cover of an RFD operator alge bra. I will connect these notions to noncommutative function theory. Time permitting\, I will discuss the notion of coactions of semigroups on opera tor algebras\, and in particular\, RFD coactions.\n LOCATION:https://researchseminars.org/talk/CMO-21w5124/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Alberto Dayan (Washington University in St. Louis) DTSTART:20210805T150500Z DTEND:20210805T155500Z DTSTAMP:20260422T185352Z UID:CMO-21w5124/8 DESCRIPTION:Title: Interpolating d-tuples of matrices\nby Alberto Dayan (Washington U niversity in St. Louis) as part of CMO workshop: Multivariable Operator T heory and Function Spaces in several Variables\n\n\nAbstract\nThe main goa l of the talk is to give an overview of some known arguments that relates interpolating sequences in a multi-variable setting to Riesz system type c onditions on reproducing kernel Hilbert spaces. The first part of the talk reviews Agler’s and McCarthy’s characterization of interpolating sequ ences in the bidisc\, and it highlights how some of those techniques apply also to a generalized interpolating problem\, in which the nodes are d-tu ples of commuting square matrices (of any dimension).\nThe second part of the talk deals with the case of sequences of eventually non commuting matr ices. We review the robust theory of noncommutative function theory on the noncommutative unit ball\, and we see how a noncommutative version of the Pick property enjoyed by the NC Drury-Arveson space gives a characterizat ion of interpolating sequences in this non commutative setting.\n LOCATION:https://researchseminars.org/talk/CMO-21w5124/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Greg Knese (Washington University in St. Louis) DTSTART:20210805T161500Z DTEND:20210805T170500Z DTSTAMP:20260422T185352Z UID:CMO-21w5124/9 DESCRIPTION:Title: Singularities of rational inner functions in higher dimensions (Bickel \, Pascoe\, Sola)\nby Greg Knese (Washington University in St. Louis) as part of CMO workshop: Multivariable Operator Theory and Function Space s in several Variables\n\n\nAbstract\nWe study the boundary behavior of ra tional inner functions (RIFs) in dimensions three and higher from both ana lytic and geometric viewpoints. On the analytic side\, we use the critical integrability of the derivative of a rational inner function of several v ariables to quantify the behavior of a RIF near its singularities\, and on the geometric side we show that the unimodular level sets of a RIF convey information about its set of singularities. We then specialize to three-v ariable degree (m\,n\,1) RIFs and conduct a detailed study of their deriva tive integrability\, zero set and unimodular level set behavior\, and non- tangential boundary values. Our results\, coupled with constructions of no n-trivial RIF examples\, demonstrate that much of the nice behavior seen i n the two-variable case is lost in higher dimensions.\n LOCATION:https://researchseminars.org/talk/CMO-21w5124/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Lukasz Kosinski (University in Krakow) DTSTART:20210806T140000Z DTEND:20210806T145000Z DTSTAMP:20260422T185352Z UID:CMO-21w5124/10 DESCRIPTION:Title: Theory of holomorphically invariant metrics in Nevalinna Pick interpo lation\nby Lukasz Kosinski (University in Krakow) as part of CMO works hop: Multivariable Operator Theory and Function Spaces in several Variabl es\n\n\nAbstract\nWe shall discuss some aspects of the theory of invariant \nfunctions and their applications to Nevanlinna Pick interpolation and\ne xtension problems\n LOCATION:https://researchseminars.org/talk/CMO-21w5124/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Dritschel (University of Newcastle) DTSTART:20210806T150500Z DTEND:20210806T155500Z DTSTAMP:20260422T185352Z UID:CMO-21w5124/11 DESCRIPTION:Title: Real Algebraic Geometry via Operator Theory\nby Michael Dritschel (University of Newcastle) as part of CMO workshop: Multivariable Operato r Theory and Function Spaces in several Variables\n\n\nAbstract\nReal alge braic geometry as a discipline was born out of Hilbert's 17th problem\, pr esented at the 1900 ICM. In it\, the primary goal is to succinctly descri be the set of polynomials which are non-negative on a semi-algebraic set ( that is\, one described by a finite set of polynomial inequalities). Unti l the 1980s\, the field was predominantly studied via logic and algebra. Konrad Schmüdgen then discovered a deep connection to analysis. More rec ently\, analysts have focused on (freely) non-commutative versions of the area's now classical problems. We emphasize the latter\, especially a few key papers of Helton and McCullough\, along with some of the work followi ng on.\n LOCATION:https://researchseminars.org/talk/CMO-21w5124/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Raphaël Clouâtre (University of Manitoba) DTSTART:20210806T161500Z DTEND:20210806T170500Z DTSTAMP:20260422T185352Z UID:CMO-21w5124/12 DESCRIPTION:Title: The Ostermann--Ransford approach to the Crouzeix conjecture\nby R aphaël Clouâtre (University of Manitoba) as part of CMO workshop: Multi variable Operator Theory and Function Spaces in several Variables\n\n\nAbs tract\nA theorem of Crouzeix implies that\, given a Hilbert space operator $T$\, its numerical range $W(T)$ is necessarily a spectral set. In other words\, upon endowing the space of polynomials with the supremum norm over $W(T)$\, the functional calculus\n\\[\np\\mapsto p(T)\, \\quad p\\in \\ma thbb{C}[z]\n\\]\nis a bounded homomorphism. What is the norm of this homom orphism?\n\nTo this day\, the precise answer is yet unknown\, although in 2007 Crouzeix conjectured it to be at most $2$. In this talk\, I will desc ribe a recent approach to the conjecture\, proposed by Ostermann and Ransf ord. Surprisingly\, this approach is very general and almost purely algebr aic: it is concerned with the interaction between finite-dimensional repre sentations and certain conjugate-linear self-maps of a uniform algebra.\n LOCATION:https://researchseminars.org/talk/CMO-21w5124/12/ END:VEVENT END:VCALENDAR