Events

Geometry, Topology, and Physics Series (GTP)

Spring 2023 Every Wednesday throughout the semester

• February 8, 2023 | Fractional structures on bundle gerbe modules and fractional classifying spaces | Ruizhi Huang

   

   
• February 1, 2023 | Simplicial, Differential, and Equivariant Homotopy Type Theory | David Jaz Myers (NYUAD)

   

  Speaker: David Jaz Myers (NYU, Abu Dhabi)

  Bio: https://nyuad.nyu.edu/en/research/faculty-labs-and-projects/cqts/david-myers.html
  

  Zoom Link
• January 25, 2023 | Representation Theory of affine vertex algebras | Thomas Creutzig (University of Alberta, Canada)

  Recently there has been increased interest in non-semisimple braided tensor categories. Vertex algebras are a rich source of such categories and so I will give an overview on the representation theory of affine vertex algebras with a focus on the simplest example of sl(2). As we will see, already in this example quite rich and non-semisimple categories of modules appear. 

  Speaker: Thomas Creutzig (University of Alberta, Canada)

  Bio: https://sites.ualberta.ca/~creutzig/
  

  Zoom Link

Fall 2022 Every Wednesday throughout the semester

• December 14, 2022 | The (∞,1)-category of Types | Eric Finster (University of Birmingham)

  A major outstanding difficulty in Homotopy Type Theory is the
  description of coherent higher algebraic structures.  As an example,
  we know that the algebraic structure possessed by the collection of
  types and functions between them is *not* a traditional 1-category,
  but rather an (∞,1)-category.  In this talk, I will describe how the
  addition of a finite collection additional definitional equalities
  designed to render the notion of "opetopic type" definable in fact
  allows one to construct the (∞,1)-category structure on the universe
  of types.

  Speaker: Eric Finster (University of Birmingham)

  Bio: https://ericfinster.github.io/
  

  Zoom Link
• December 7, 2022 | Infinity-category theory for undergraduates | Emily Riehl (Johns Hopkins University)

  At its current state of the art, infinity-category theory is challenging to explain even to specialists in closely related mathematical areas. Nevertheless, historical experience suggests that in, say, a century's time, we will routinely teach this material to undergraduates. This talk describes one dream about how this might come about --- under the assumption that 22nd century undergraduates have absorbed the background intuitions of homotopy type theory/univalent foundations.

  Speaker: Emily Riehl (Johns Hopkins University)

  Bio: https://emilyriehl.github.io
  

  Zoom Link
• November 30, 2022 | Classification and double commutant property for dual pairs in an orthosymplectic Lie supergroup. | Allan Merino (University of Ottawa)

  At its current state of the art, infinity-category theory is challengingto explain even to specialists in closely related mathematical areas.Nevertheless, historical experience suggests that in, say, a century'stime, we will routinely teach this material to undergraduates. This talkdescribes one dream about how this might come about --- under theassumption that 22nd century undergraduates have absorbed the backgroundintuitions of homotopy type theory/univalent foundations.

  Speaker: Allan Merino (University of Ottawa)

  Bio: http://allanmerino.com/
  

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• November 23, 2022 | Brownian loops and conformally invariant systems | Valentino Foit (NYUAD)

  This talk aims to convey why I am excited about the potential of some variant homotopy type theory as a foundation for higher category theory. This will be illustrated by a case study involving the Yoneda lemma for (oo,1)-categories. In homotopy type theory, the contractibility of the based path space is expressed by the principle of "path induction," which says that identity types are freely generated by reflexivity terms. By an analogy in which arrows in an (oo,1)-category are thought of as directed paths, there is an analogous principle of "arrow induction," which says that hom types are freely generated by identity arrows. We explain how this unravels to a "dependent" generalization of the Yoneda lemma. This involves joint work with Dominic Verity and Mike Shulman.

  Speaker: Valentino Foit (NYUAD)

  Bio: https://inspirehep.net/authors/1395407
  

  Zoom Link
• November 9, 2022 | Twisted Real quasi-elliptic cohomology | Zhen Huan (Center for Mathematical Sciences, Huazhong University of Science and Technology, China)

  Quasi-elliptic cohomology is closely related to Tate K-theory. It is constructed as an object both reflecting the geometric nature of elliptic curves and more practicable to study than most elliptic cohomology theories. It can be interpreted by orbifold loop spaces and expressed in terms of equivariant K-theories. We formulate the complete power operation of this theory. Applying that we prove the finite subgroups of Tate curve can be classified by the Tate K-theory of symmetric groups modulo a certain transfer ideal. In this talk we construct twisted Real quasi-elliptic cohomology as the twisted KR-theory of loop groupoids. The theory systematically incorporates loop rotation and reflection. After establishing basic properties of the theory, we construct Real analogues of the string power operation of quasi-elliptic cohomology. We also explore the relation of the theory to the Tate curve. This is joint work with Matthew Young

  Speaker: Zhen Huan (Center for Mathematical Sciences, Huazhong University of Science and Technology, China)

  Bio:
  

  Zoom Link
• October 26, 2022 | Quantum programming via linear homotopy types | Urs Schreiber (CQTS, NYUAD)

  Long Description

  Speaker: Urs Schreiber (CQTS, NYUAD)

  Bio: Visit Urs Schreiber's Website

   

• October 19, 2022 | Topological Wick Rotation and Holographic duality| Liang Kong (SUSTech, Southern University of Science and Technology, China)

  I will explain a new type of holographic dualities between (n+1)D topological orders with a chosen boundary condition and nD (potentially gapless) quantum liquids. It is based on the idea of topological Wick rotation, a notion which was first used in arXiv:1705.01087 and was named, emphasized and generalized later in arXiv:1905.04924. Examples of these holographic dualities include the duality between (2+1)D toric code model and (1+1)D Ising chain and its finite-group generalizations (independently discovered by many others); those between (2+1)D topological orders and (1+1)D rational conformal field theories; and those between (n+1)D finite gauge theories with a gapped boundary and nD gapped quantum liquids. I will also briefly discuss some generalizations of this holographic duality and its relation to AdS/CFT duality

  Speaker: Liang Kong (SUSTech, Southern University of Science and Technology, China)

  Bio:
  

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• October 12, 2022 | Algebraic and geometric aspects of the Dirac equation | Salah Mehdi (Université de Lorraine and NYUAD)

  The equation appeared in a 1928 paper written by Nobel prize laureate Paul Dirac. It describes the quantum dynamics of the electron on the Minkowski spacetime. In this talk, I will first extend Dirac equation to bundles over homogeneous manifolds, then I will explain how one can use geometric and algebraic tools to solve the equation.

  Speaker: Salah Mehdi (Université de Lorraine and NYUAD)

  Bio: Visit Salah Mehdi's Website

   

• October 5, 2022 | The smooth Oka principle | Adrian Clough (NYUAD)
  The infinity topos of differentiable sheaves contains all smooth manifolds as a full subcategory and has excellent formal properties. In particular, it admits an intrinsic notion of underlying homotopy type of any differentiable sheaf, which coincides with classical constructions such as taking smooth total singular complexes. Moreover, there is a canonical sense in which the mapping sheaf between any two differentiable sheaves may have the correct homotopy type. This latter notion is reminiscent of the Oka principle in complex geometry. In this talk I will show how to exhibit the Oka principle in the smooth setting using model structures and other homotopical calculi on the infinity topos of differentiable sheaves.

  Speaker: Adrian Clough (NYUAD)

  Bio: Christopher Adrian Clough's Website

   

  Zoom Link
• September 28, 2022 | Objective twisted cohomology: towards topological quantum computation | David Jaz Myers (NYUAD)
  In this talk, we will see the homotopy type theory point of view on defining twisted cohomology classes by means of bundle gerbes. We'll take an increasingly less leisurely tour up the tower of cohomology degrees, seeing characters, principal
  bundles, central extensions, and characteristic classes along the way. Finally, we will go through the construction of the cohomology of the braid groups valued in the complex numbers, twisted by a complex character of the braid group. Through the work of many
  people, and in particular Feigin, Schechtman, Varchenko, the actions of the braid group of d "defects" on the twisted complex cohomology of the braid group of n "particles" is the monodromy action of the Knizhnik-Zamolodchikov connection on a space of
  conformal blocks, giving a way of passing from abstract homotopy type theory to protocols for topological quantum computation.

  Speaker: David Jaz Myers

  Bio: Visit David Myers' Website

   

• September 21, 2022 | Braided Homotopy Lie Algebras and Noncommutative Field Theories | Grigorios Giotopoulos (NYUAD)

  Long Description:

  Speaker: Grigorios Giotopoulos (NYUAD)

  Bio: 
  

The Quantum Colloquium

Spring 2023 Every Monday throughout the semester

• January 30, 2023 | Chern-Simons theory, Knot polynomials & Quivers | Vivek Singh (NYUAD)

  First, I will give a brief introduction to knot theory and its connection to Chern-Simons quantum field theory. Then discuss the method of obtaining polynomial invariants and limitations towards tackling classification of knots. In particular, we will highlight our new results on weaving knots and review the recent developments on Knot-Quiver correspondence.

  Speaker: Vivek Singh (NYUAD)

  Bio: https://nyuad.nyu.edu/en/research/faculty-labs-and-projects/cqts/researchers/vivek-kumar-singh.html

  Zoom Link

Fall 2022 Every Monday throughout the semester

• December 12, 2022 | Quantum Algorithms, from noisy intermediate scale devices through the early fault-tolerant era | Leandro Aolita (Quantum Research Center, Technology Innovation Institute TII)

  Reaching long-term maturity in quantum computation science and technology relies on the field delivering practically useful application in a short term. In this colloquium, I will discuss ideas for the  noisy intermediate scale (NISQ) and early fault-tolerant eras. I will divide my talk into two parts. In the first part, I will make a brief non-technical introduction to the field, its relevance to the UAE, and the main lines of research of the Quantum Algorithms division at QRC-TII. 

  In the second one, I will try to convey some level of technical detail about our work. In particular, I will first present a hybrid classical-quantum algorithm to simulate high-connectivity quantum circuits from low-connectivity ones. This provides a versatile toolbox for both error-mitigation and circuit boosts useful for NISQ computations. Then, I will move on to algorithms for the forthcoming quantum hardware of the early fault-tolerant era: I will present a new generation of high-precision algorithms for simulating quantum imaginary-time evolution (QITE) that are significantly simpler than current schemes based on quantum amplitude amplification (QAA). QITE is central not only to ground-state optimisations but also to partition-function estimation and Gibbs-state sampling, with a plethora of computational applications. 

  Speaker: Leandro Aolita (Quantum Research Center, Technology Innovation Institute TII, Abu Dhabi)

  Bio: https://www.tii.ae/team/prof-leandro-aolita-about-us
  

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• November 28, 2022 | Development of molecular spin qubits | Asif Equbal (Chemistry, NYUAD)

  Spins are a purely quantum mechanical phenomenon and have been proposed as one of the several candidates for qubits in quantum information science. Quantum computers based on spin qubits were first proposed by DiVincenzo, who established five necessary criteria for building a quantum computer. The technology to control the quantum states of nuclear and electron spins and the theory of spin-spin and spin-magnetic field interactions are well developed, but a quantum computer based on spin qubits has not yet been realized. Why is this?

  In this talk, I will discuss the challenges in developing spin qubits that meet DiVincenzo's criteria for quantum computers. First, I will explain in a pedagogical way how to manipulate spins in an external magnetic field that form the building block of quantum logic gates. I will then provide some insight into my own recent research on the development of optically polarized molecular spin qubits in solids.
  

  Speaker: Asif Equbal (Chemistry, NYUAD)

  Bio: Visit Asif Equbal's website

   

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• November 21, 2022 | A new spin on magnetism with applications in information processing | Andy Kent (Center for Quantum Phenomena, NYU)

  Recent advances in magnetism research are likely to have an important impact on electronicsand information processing. These advances use the electron magnetic moment (spin) to transmit, write and store information. They enable new devices that operate at high speed with very low energy consumption. The information is stored in the orientation of electron magnetic moments in magnetic materials and can persist without power; energy is only needed to write and read the information. Important physics concepts include the interconversion of electrical (charge) currents into spin currents, the efficiency of the interconversion, controlling the currents' spin polarization direction, and the associated spin torques on magnetic order. Magnetic skyrmions are also of interest both because of their stability --- they are topologically protected objects --- and because their nucleation and motion can be controlled using spin currents. In this talk I will highlight the new physics concepts that have enabled these advances and discuss some of their applications in information processing.

  Speaker: Andrew Kent (NYU)

  Bio: https://as.nyu.edu/faculty/andrew-d-kent.html
  

  Zoom Link
• November 7, 2022 | How to realise exotic particle statistics | Jiannis Pachos (Leeds University, UK)

  Combining physics, mathematics and computer science, topological quantum information [1] is a rapidly expanding field of research focused on the exploration of quantum evolutions that are resilient to errors. In this talk I will present a variety of different topics starting from introducing anyonic models, topological phases of matter, Majorana fermions, characterising knot invariants, their quantum simulation with anyons and finally the possible realisation of anyons in the laboratory. [1] J. K. Pachos, Introduction to Topological Quantum Computation, Cambridge University Press, 2012.

  Speaker: Jiannis Pachos (Leeds University, UK)

  Bio: https://theory.leeds.ac.uk/jiannis-pachos/
  

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• October 31, 2022 | Quantum Walks in the Presence of Local Fields | Houssam Abdul Rahman (Math, NYUAD)

  Quantum Walks are the quantum generalizations of classical random walks where the transitions of the quantum particle are done via unitary evolutions. They exhibit very different features than their classical counterparts, for example, they may spread significantly faster than random walks. Quantum walks are powerful tools for quantum computing, and they provide advanced methods in building quantum algorithms. 

  Speaker: Houssam Abdul Rahman (Math, NYUAD)

  Bio: Houssam Abdul Rahman's Website

   

• October 10, 2022 | Topological quantum states for quantum computing and metrology | Tim Byrnes (NYUSH)
  Zoom Link

  Long Description

  Speaker: Tim Byrnes (NYUSH)

  Bio: