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PRODID:Mathematics Seminar Calendar
BEGIN:VEVENT
UID:20221205T020311-29401@math.msu.edu
DTSTAMP:20221205T020311Z
SUMMARY:Making Weight
DESCRIPTION:Speaker\: Brent Nelson, MSU\r\nA weight on a von Neumann algebra is a positive linear map that is permitted to be infinitely valued. It is a generalization of a positive linear functional that arises naturally in the context of crossed products by non-discrete groups, and they are vital to the study of purely infinite von Neumann algebras. In this talk I will provide an introduction to the theory of weights that assumes only the definition of a von Neumann algebra.
LOCATION:C517 Wells Hall
DTSTART:20220912T200000Z
DTEND:20220912T213000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29401
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BEGIN:VEVENT
UID:20221205T020311-29424@math.msu.edu
DTSTAMP:20221205T020311Z
SUMMARY:Worth Their Weight
DESCRIPTION:Speaker\: Brent Nelson, MSU\r\nI will continue my introduction to weights. I will briefly mention equivalent conditions of normality for weights before moving onto a discussion of semi-cyclic representations and Tomita-Takesaki theory. I will conclude with a detailed examination of Plancherel weights on locally compact groups.
LOCATION:C517 Wells Hall
DTSTART:20220919T200000Z
DTEND:20220919T213000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29424
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BEGIN:VEVENT
UID:20221205T020311-29408@math.msu.edu
DTSTAMP:20221205T020311Z
SUMMARY:Conjugate Variables and Dual Systems
DESCRIPTION:Speaker\: Aldo Garcia Guinto, MSU\r\nIn free probability, the semi-circular operators are the analogue of the Gaussian distribution in classical probability. We will be using the semi-circular operators to motivate two notions of free probability: conjugate variables and dual systems. The conjugate variables are used to define free Fisher information, which is analogue of Fisher information in classical probability. While the dual systems are related to a cohomology theory for von Neumann algebras. It turns out that these two notions are not as different as they may seem.
LOCATION:C517 Wells Hall
DTSTART:20220926T200000Z
DTEND:20220926T213000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29408
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BEGIN:VEVENT
UID:20221205T020311-29439@math.msu.edu
DTSTAMP:20221205T020311Z
SUMMARY:Introduction to Graph Algebras
DESCRIPTION:Speaker\: Lucas Hall, MSU\r\nWe introduce directed graphs and demonstrate how to generate a C*-algebra which reflects certain features of the graph. Time permitting, we will introduce two uniqueness theorems for their representations and explore a few of their consequences.
LOCATION:C517 Wells Hall
DTSTART:20221003T200000Z
DTEND:20221003T213000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29439
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BEGIN:VEVENT
UID:20221205T020311-29440@math.msu.edu
DTSTAMP:20221205T020311Z
SUMMARY:Graph algebras: universality, uniqueness, and ideal structure
DESCRIPTION:Speaker\: Lucas Hall, MSU\r\nWe illustrate various aspects of graph algebras introduced last week, including usage of the universal property, aspects of their representation theory, and ideals, pointing to relationships with the structure of the underlying graph.
LOCATION:C517 Wells Hall
DTSTART:20221010T200000Z
DTEND:20221010T213000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29440
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BEGIN:VEVENT
UID:20221205T020311-30489@math.msu.edu
DTSTAMP:20221205T020311Z
SUMMARY:Free transport, I
DESCRIPTION:Speaker\: Brent Nelson, MSU\r\nIn operator algebras, specifically free probability, free transport is a technique for producing state-preserving isomorphisms between C* and von Neumann algebras that was developed by Guionnet and Shlyakhtenko in their 2014 Inventiones paper. The inspiration for their work comes from the field of optimal transport, specifically work of Brenier from 1991 who showed that under very mild assumptions one can push forward a probability measure on $\mathbb{R}^n$ to the Gaussian measure. In the non-commutative case, Guionnet and Shlyakhtenko showed that if $x_1,\ldots, x_n$ are self-adjoint operators in a tracial von Neumann algebra $(M,\tau)$ whose distribution satisfies an "integration-by-parts" formula up to a small perturbation, then these operators generate a copy of the free group factor $L(\mathbb{F}_n)$. In this series of talks, I will give an overview of their proof, discuss some applications of their result, and survey the current state of free transport theory.
LOCATION:C517 Wells Hall
DTSTART:20221107T210000Z
DTEND:20221107T223000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=30489
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BEGIN:VEVENT
UID:20221205T020311-30496@math.msu.edu
DTSTAMP:20221205T020311Z
SUMMARY:Free transport, II
DESCRIPTION:Speaker\: Brent Nelson, MSU\r\nIn operator algebras, specifically free probability, free transport is a technique for producing state-preserving isomorphisms between C* and von Neumann algebras that was developed by Guionnet and Shlyakhtenko in their 2014 Inventiones paper. The inspiration for their work comes from the field of optimal transport, specifically work of Brenier from 1991 who showed that under very mild assumptions one can push forward a probability measure on $\mathbb{R}^n$ to the Gaussian measure. In the non-commutative case, Guionnet and Shlyakhtenko showed that if $x_1,\ldots, x_n$ are self-adjoint operators in a tracial von Neumann algebra $(M,\tau)$ whose distribution satisfies an "integration-by-parts" formula up to a small perturbation, then these operators generate a copy of the free group factor $L(\mathbb{F}_n)$. In this series of talks, I will give an overview of their proof, discuss some applications of their result, and survey the current state of free transport theory.
LOCATION:C517 Wells Hall
DTSTART:20221114T210000Z
DTEND:20221114T223000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=30496
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BEGIN:VEVENT
UID:20221205T020311-31501@math.msu.edu
DTSTAMP:20221205T020311Z
SUMMARY:Modular Stone-von Neumann Theorems
DESCRIPTION:Speaker\: Lucas Hall, MSU\r\nI’ll talk about C*-modules and representations on them, developing a loose parallel with the Hilbert space case. For specialized C*-modules, much can be said, and a classification of these modules suggests a vast generalization of the Stone-von Neumann Theorem which accommodates all of the data of generalized C*-dynamical systems.
LOCATION:C517 Wells Hall
DTSTART:20221121T210000Z
DTEND:20221121T223000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=31501
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BEGIN:VEVENT
UID:20221205T020311-29441@math.msu.edu
DTSTAMP:20221205T020311Z
SUMMARY:An Introduction to K-theory
DESCRIPTION:Speaker\: Matthew Lorentz, MSU\r\nBased on the work of Grothendieck, in the 1960's Atiyah and Hirzebruch developed K-theory as a tool for algebraic geometry. Adapted to the topological setting K-theory can be regarded as the study of a ring generated by vector bundles. In the 1970's it was introduced as a tool in C*-algebras. C*-algebras are often considered to be "noncommutative topology", additionally they are an algebra over the complex numbers. In this setting the algebraic and topological definitions of K-theory overlap giving us a powerful tool. Essential for the Elliott classification program, for certain classes of C*-algebras, K-theory is a complete invariant. K-theory is also a natural setting for higher index theory.\r\n\r\nWe will begin by looking at different types of equivalence for projections. Then we will build a monoid where these types of equivalences are equivalent. We then use the Grothendieck construction to turn our monoid into an abelian group. This group is called the $K_0$ group of our algebra and can be thought of as the "connected components" of projections in our C*-algebra.\r\n\r\nNext, in a similar manner, we construct the $K_1$ group using unitaries from our C*-algebra. \r\nOnce we have the $K_0$ and $K_1$ groups we will discuss Bott periodicity and the six-term exact sequence, a tool used to calculate K-theory.
LOCATION:C517 Wells Hall
DTSTART:20221128T210000Z
DTEND:20221128T223000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=29441
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BEGIN:VEVENT
UID:20221205T020311-30479@math.msu.edu
DTSTAMP:20221205T020311Z
SUMMARY:The Integrated Density of States and the Gap Labeling Theorem via "K-Theory"
DESCRIPTION:Speaker\: Alberto Takase, MSU\r\nMy talk will be about the Integrated Density of States and the Gap Labeling Theorem via "K-Theory". The primary source is Bellissard, Jean; Bovier, Anton; Ghez, Jean-Michel \textit{Gap labelling theorems for one-dimensional discrete Schrödinger operators}. Rev. Math. Phys. 4 (1992), no. 1, 1–37.
LOCATION:C517 Wells Hall
DTSTART:20221205T210000Z
DTEND:20221205T223000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=30479
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