Events

Geometry, Topology, and Physics Series (GTP)

Spring 2023 Every Wednesday throughout the semester

• May 3, 2023 | n-Complicial sets as a model for (oo,n)-categories | Martina Rovelli (University of Massachusetts, Amherst, USA)

  The formalism of extended TQFTs relies the notion of an (oo,n)-category: a categorical structure with morphisms in each dimension, which can be composed in a weakly associative way, and which are weakly invertible in dimension higher than n. In this expository talk I will describe the notion of an n-complicial set, explain the intuition for how this implements the idea of an (oo,n)-category, and discuss some of the advantages and disadvantages of this approach.

  Speaker: Martina Rovelli (University of Massachusetts, Amherst, USA)

  Bio: https://people.math.umass.edu/~rovelli/
  

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• April 26, 2023 | Stability patterns for braid groups and configuration spaces | Jenny Wilson (University of Michigan)

  This talk will give an introduction of the field of 'representation stability'. I will discuss how we can use representation theory to illuminate the structure of certain families of groups or topological spaces with actions of the symmetric groups, focusing on braid groups and configuration spaces as motivating examples.

  Speaker: Jenny Wilson (University of Michigan, USA)

  Bio: https://dept.math.lsa.umich.edu/~jchw/
  

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• April 19, 2023 | A bulk-boundary correspondence with factorization algebras | Owen Gwilliam (University of Massachusetts, Amherst, USA)

  Factorization algebras provide a flexible language for describing the observables of a perturbative quantum field theory, as shown in joint work with Kevin Costello. In joint work with Eugene Rabinovich and Brian Williams, we extended those constructions to a manifold with boundary for a special class of theories that includes, as an example, a perturbative version of the correspondence between chiral U(1) currents on a Riemann surface and abelian Chern-Simons theory on a bulk 3-manifold. (These methods extend to interacting theories, thanks to the thesis of Rabinovich. ) Given time, I'll sketch a systematic higher dimensional version for higher abelian CS theory on an oriented smooth manifold of dimension 4n+3 with boundary a complex manifold of complex dimension 2n+1. The talk is expository, and it can be redirected according to the audience's interests and requests.

  Speaker: Owen Gwilliam (University of Massachusetts, Amherst, USA)

  Bio: https://www.msri.org/people/21444
  

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• April 12, 2023 | The spinor bundle on loop space and its fusion product | Matthias Ludewig (University of Regensburg, Germany)

  We will discuss the definition of the spinor bundle on loop space and the construction of its fusion product, as suggested in a 2005 preprint by Stolz and Teichner. This is based on work by Kristel and Waldorf, involving some simplifications and additions due to myself.

  Speaker: Matthias Ludewig (University of Regensburg, Germany)

  Bio: https://homepages.uni-regensburg.de/~lum63364/
  

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• April 5, 2023 | Relating cut and paste invariants and TQFTS | Carmen Rovi (Loyola University, Chicago)

  In this talk, we will be concerned with a relation between TQFTs and the cut-and-paste SKK  invariants introduced by Karras, Kreck, Neumann, and Ossa. Cut-and-paste SKK  invariants are functions on the set of smooth manifolds whose values on cut-and-paste equivalent manifolds differ by an error term depending only on the gluing diffeomorphisms. I will present a natural group homomorphism between the group of invertible TQFTs and the group of SKK  invariants and describe how these groups fit into a split exact sequence. We conclude in particular that all positive real-valued SKK  invariants can be realized as restrictions of invertible TQFTs.

  Speaker: Carmen Rovi (Loyola University, Chicago)

  Bio: https://www.luc.edu/math/ftfaculty/rovicarmen.shtml
  

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• March 29, 2023 | Quinn Finite Total Homotopy TQFT as a once-extended TQFT | Joao Faria Martins (Leeds University, UK)

  Quinn Finite Total Homotopy TQFT is a TQFT defined for any dimension, $n$, of space, and that depends on the choice of a homotopy finite space, $B$, (e.g. $B$ can be the classifying space of a finite group or of a finite 2-group). I will report on ongoing joint work with Tim Porter on once-extended versions of Quinn Finite total homotopy TQFT, taking values in the (symmetric monoidal) bicategory of groupoids, linear profunctors, and natural transformations between profunctors. The construction works in all dimensions, thus in particular it yields (0,1,2), (1,2,3) and (2,3,4)-extended TQFTs, any time we are given a homotopy finite space $B$. I will show how to compute these once-extended TQFTs for the case when $B$ is the classifying space of a finite strict omega-groupoid, represented by a crossed complex.

  Main reference: Faria Martins J, Porter T : A categorification of Quinn's finite total homotopy TQFT with application to TQFTs and once-extended TQFTs derived from strict omega-groupoids. arXiv:2301.02491 [math.CT]. (235 pages, preliminary version.)

  Speaker: João Faria Martins (Leeds University, UK)

  Bio: http://www1.maths.leeds.ac.uk/~pmtjfa/
  

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• March 8, 2023 | Geometric Hodge filtered complex cobordism | Gereon Quick (Norwegian University of Science and Technology)

  Differential cohomology theories on smooth manifolds play an important role in mathematical physics and other areas of mathematics. In their seminal work, Hopkins and Singer showed that every topological cohomology theory has a differential refinement. In this talk, I will first report on joint work with Mike Hopkins on a similar refinement of complex cobordism on complex manifolds which takes the Hodge filtration into account. I will then present joint work with Knut Haus in which we give a concrete geometric cycle model for this theory. This allows us to give a concrete description of an Abel-Jacobi type secondary invariant for topologically trivial cobordism cycles.

  Speaker: Gereon Quick (Norwegian University of Science and Technology)

  Bio: https://www.ntnu.edu/employees/gereon.quick
  

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• March 1, 2023 | Deformation quantization and categorical factorization homology | Lukas Mueller (Perimeter Institute for Theoretical Physics, Canada)

  Moduli spaces of flat principal bundles on surfaces are a prominent object in mathematical physics, algebraic geometry and geometric representation theory. In particular they are the phase space of 3-dimensional Chern-Simons theory on a surface times an interval and hence equipped with a symplectic structure going back to the work of Atiyah and Bott. Various deformation quantizations of the algebra of functions have been constructed. Ben-Zvi Brochier Jordan constructed `local to global' quantizations using factorization homology of representation categories of quantum groups. Local to global constructions in this setting only work if the higher geometric structure of the moduli space of flat bundles is taken into account, i.e. it is treated as a moduli stack. In this setting the algebra of functions does not contain all the information and should be replaced by the category of quasi coherent sheaves.
  In my talk we will explore categorifications of deformation quantization as deformations of symmetric monoidal categories (algebras over the E_oo-operad) into E_i-categories and their interplay with factorization homology. The main result is that 2-dimensional factorization homology `commutes' with quantization in a way relating E_0-quantizations to braided (E_2) quantizations. We will illustrate our results with examples from Poisson geometry and quantum groups. As a specific application we show that deformation quantizations of the moduli space of flat bundles based on Kontsevich integrals constructed by Li-Bland and Ševera are equivalent to quantizations constructed by Alekseev, Grosse, Schomerus based on quantum groups. The talk is based on joint work in progress with Eilind Karlsson, Corina Keller, and Jan Pulmann.  

  Speaker: Lukas Mueller (Perimeter Institute for Theoretical Physics, Canada)

  Bio: https://sites.google.com/view/lukas-mueller/home
  

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• February 22, 2023 | Applied and Computational Topology | Dmitry Kozlov (University of Bremen, Germany)

  We will give a brief introduction to the subject of Applied and Computational Topology. The survey of the subject's main ideas and tools will be complemented with applications to discrete mathematics and to theoretical distributed computing. We will conclude with stating an open problem in combinatorial topology which is related to the complexity of the Weak Symmetry Breaking distributed task.

   

  Speaker: Dmitry Kozlov (University of Bremen, Germany) 

  Bio: https://scholar.google.co.il/citations?user=ZMc1jGQAAAAJ&hl=en
  

   

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• February 15, 2023 | Classical Bulk-Boundary Correspondences via Factorization Algebras | Eugene Rabinovich (University of Notre Dame, USA)

  A factorization algebra is a cosheaf-like local-to-global object which is meant to model the structure present in the observables of classical and quantum field theories. 
  In the Batalin-Vilkovisky (BV) formalism, one finds that a factorization algebra of classical observables possesses, in addition to its factorization-algebraic structure, a compatible Poisson bracket of cohomological degree +1.  Given a ``sufficiently nice'' such factorization algebra on a manifold $N$, one may associate to it a factorization algebra on $N\times \mathbb{R}_{\geq 0}$.
  
  The aim of the talk is to explain the sense in which the latter factorization algebra ``knows all the classical data'' of the former.
  
  This is the bulk-boundary correspondence of the title.  Time permitting, we will describe how such a correspondence appears in the deformation quantization of Poisson manifolds.
  

   

  Speaker: Eugene Rabinovich (University of Notre Dame, USA) 

  Bio: https://math.nd.edu/people/faculty/eugene-rabinovich/
  

   

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• February 8, 2023 | Fractional structures on bundle gerbe modules and fractional classifying spaces | Ruizhi Huang (Chinese Academy of Sciences)

  Both higher structures and bundle grebe modules play important roles in modern geometry and mathematical physics. Bundle gerbe module is a twisted version of vector bundles, and was introduced by Bouwknegt-Carey-Mathai-Murray-Stevenson in 2002. In particular, they introduced the twisted Chern character from the perspective of Chern-Weil theory.

  In a recent joint work with Han and Mathai, we study the homotopy aspects of the twisted Chern classes of torsion bundle gerbe modules. Using Sullivan's rational homotopy theory, we realize the twisted Chern classes at the level of classifying spaces. The construction suggests a notion, which we call fractional U-structure serving as a universal framework to study the twisted Chern classes of torsion bundle gerbe modules from the perspective of classifying spaces. Based on this, we introduce and study higher fractional structures on torsion bundle gerbe modules parallel to the higher structures on ordinary vector bundles.

  Speaker: Ruizhi Huang

  Bio: https://sites.google.com/site/hrzsea/
  

   

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• 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
  

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• 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/
  

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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/
  

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• 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
  

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• 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
  

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• 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:
  

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

   

  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

   

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• 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)

   

  Speaker: Grigorios Giotopoulos (NYUAD)

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

The Quantum Colloquium

Spring 2023 Every Monday throughout the semester

• May 8, 2023 | Optimal control of large spin systems | Ilya Kuprov (University of Southampton)

  In magnetic resonance, optimal control theory is used to generate pulses and pulse sequences that achieve instrumentally difficult objectives (for example, uniform 13C excitation in a 1.2 GHz magnet) with high precision under stringent time and radiofrequency/microwave power constraints. At the moment, the most popular framework is GRAPE (gradient ascent pulse engineering, 10.1016/j.jmr.2004.11.004). This lecture reports our recent mathematical and software engineering work on the various extensions and refinements of the GRAPE framework, and on its implementation as a module of Spinach library. Recently implemented functionality includes: fidelity Hessians and regularised Newton-Raphson optimisation, generalised curvilinear waveform parametrisation, prefix and suffix pulse sequences, multi-target and subspace control, keyhole states and subspaces, cooperative pulses and phase cycles, and piecewise-linear control sequences. In keeping with the long tradition, the methods are also directly applicable to quantum technologies outside Magnetic Resonance.

  Speaker: Ilya Kuprov (University of Southampton)

  Bio: https://www.southampton.ac.uk/people/5x97wv/doctor-ilya-kuprov

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• May 1, 2023 | High-fidelity universal quantum computation with symmetric qubit clusters | Hichem El Euch (American University of Sharjah, UAE)

  Designing a physical device that maintains the error rate for each quantum processing operation low is one of the most arduous issues for the implementation of a scalable quantum computer. These errors may result from inaccurate quantum manipulation, such as a gate voltage sweeping in solid-state qubits or a laser pulse duration. Decoherence is usually a manifestation of the interaction with the environment, and it is an entity of the quantum system which generates errors. Small clusters of qubits with symmetries can be used to shield part of them from decoherence. We encode pairs of connected qubits and universal 2-qubit logical gates using 4-level cores with omega-rotation invariance. We show that symmetry renders logical operations particularly resistant to anisotropic qubit rotations that models some quantum errors. We suggest a scalable method for universal quantum processing in which cores act as quansistors, or quantum transistors. By adjusting their intrinsic variables, quansistors may be dynamically isolated from their environment, providing them the adaptability needed to function as controlled quantum memory units.

  Speaker: Hichem El Euch (American University of Sharjah, UAE)

  Bio: https://www.sharjah.ac.ae/en/academics/Colleges/Sciences/dept/ap/Pages/ppl_detail.aspx?mcid=50

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• April 24, 2023 | Alice through the looking glass: cavity optomechanics for the study of the foundation of quantum mechanics | Mauro Paternostro ((Queen's University Belfast, Ireland))

  I will illustrate how cavity optomechanics is helping us addressing deep questions on our understanding of the foundations of quantum theory, from non-equilibrium quantum dynamics to the collapse of the wave-function. Towards the end of my talk, I will propose an optomechanical pathway for the exploration of the potential quantum nature of gravity

   

  Speaker: Mauro Paternostro (Queen's University Belfast, Ireland)

  Bio: https://pure.qub.ac.uk/en/persons/mauro-paternostro

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• April 17, 2023 | Knots-quivers correspondence: summary and update | Piotr Sułkowski (University of Warsaw, Poland)

  In this talk I will review the knots-quivers correspondence
  and mention some recent developments in this regard. The knots-quivers
  correspondence is the statement that various invariants associated to
  a knot are encoded in the corresponding quiver. This statement follows
  from engineering both knots and quivers in related brane systems in
  string theory. Recent developements, which I will mention at least
  briefly, include understanding the structure of various quivers that
  correspond to the same knot, using topological recursion to determine
  quiver generating series and corresponding quiver A-polynomias, and
  finding a quiver representation of so-called Z-hat invariants.

  Speaker: Piotr Sułkowski (University of Warsaw, Poland)

  Bio: https://scholar.google.nl/citations?user=qKCk4JMAAAAJ&hl=en

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• April 10, 2023 | Classical simulators as quantum error mitigators via circuit cutting | Zain Saleem (Argonne National Lab, USA)

  Quantum networks are pursued as a quantum backbone on which to perform secure quantum communications, distributed quantum sensing, and blind quantum computation. The building blocks of these networks are quantum repeaters, where photonic quantum information carriers are generated and error corrected through interactions with matter qubits. I will describe two paradigms of quantum repeaters and discuss in each case how careful control of a register of spin qubits can increase the entanglement distribution rate over the network. Specifically, I will describe our recent work on the accurate and fast control of nuclear spin memory qubits coupled to spin defects such as the NV center in diamond. I will also discuss the deterministic generation of photonic ‘graph’ states from such quantum emitters.

  Speaker: Zain Saleem (Argonne National Lab, USA)

  Bio: https://www.anl.gov/profile/zain-hamid-saleem

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• April 3, 2023 | Diamond-based quantum sensor for molecular analytics | Mouzhe Xie (University of Chicago)

  Quantum sensing technologies enable some of the most precise measurements that human beings have ever achieved. In recent years, optically addressable nitrogen-vacancy (NV) color center hosted by diamond crystal has been used as a novel quantum sensor, which has exquisitely sensitive response to local magnetic field fluctuations. It is therefore capable to perform micro-/nano-scale NMR experiments, manifesting enormous potential to study biological systems on extremely small sample
  volume – even down to single-molecule regime.
  
  In this seminar, I will discuss some of the comprehensive efforts to develop NV-based quantum sensing platforms for a wide range of applications in chemistry and biology. I will start with a general introduction to quantum sensing followed by conventional NMR spectroscopy as a powerful tool to study biomolecules, as well as their connections to the NV-based nanoscale NMR. I will then introduce a biocompatible surface functionalization architecture for interfacing a diamond quantum sensor with individual intact biomolecules under physiological conditions. A sensing modality based on diamond membrane integrated with flow channel will also be discussed, which is a promising platform for a variety of experiments at molecular, cellular, and even living-organism levels.

  Finally, I will conclude by providing an outlook on how NV-based quantum sensing platforms, combined with other advanced spectroscopy and microscopy methods, can be utilized to address important biophysical and bioanalytical questions with unprecedented sensitivity and spatial resolution, which will enhance our understanding of molecular interactions and cellular processes and ultimately improve human health.

  Bio: https://scholar.google.com/citations?user=Ec91cuwqYukC&hl=en
  

   

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• April 3, 2023 | Control and distribution of entanglement in quantum networks | Sophia Economou (Center for Quantum Information Science and Engineering, Virginia Tech, USA)

  Quantum networks are pursued as a quantum backbone on which to perform secure quantum communications, distributed quantum sensing, and blind quantum computation. The building blocks of these networks are quantum repeaters, where photonic quantum information carriers are generated and error corrected through interactions with matter qubits. I will describe two paradigms of quantum repeaters and discuss in each case how careful control of a register of spin qubits can increase the entanglement distribution rate over the network. Specifically, I will describe our recent work on the accurate and fast control of nuclear spin memory qubits coupled to spin defects such as the NV center in diamond. I will also discuss the deterministic generation of photonic ‘graph’ states from such quantum emitters.

  Speaker: Sophia Economou (Center for Quantum Information Science and Engineering, Virginia Tech, USA)

  Bio: https://www.phys.vt.edu/About/people/Faculty/sophia-economou.html

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• March 27, 2023 | Quantum Software | Matthias Christandl (Centre for the Mathematics of Quantum Theory, University Copenhagen, Denmark)

  In these days, we are witnessing amazing progress in both the variety and quality of platforms for quantum computation and quantum communication. Since algorithms and communication protocols designed for traditional 'classical' hardware do not employ the superposition principle and thus provide no gain even when used on quantum hardware, we are in need of developing specific quantum algorithms and quantum communication protocols that make clever use of the superposition principle and extract a quantum advantage. "Quantum hardware needs quantum software", so to say. Furthermore, due to noise in the qubits, known as decoherence, an additional quantum-specific software layer is required that emulates a perfect quantum machine on top of a noise one. I will demonstrate our recent work on this subject with theorems as well data from university and commercial quantum devices. 

  Speaker: Matthias Christandl (Centre for the Mathematics of Quantum Theory, U. Copenhagen, Denmark)

  Bio: https://www.math.ku.dk/english/staff/?pure=en/persons/475476

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• March 13, 2023 | Detecting topological order from modular transformations of ground states on the torus | Roger Mong (Pittsburgh Quantum Institute, USA)

  Speaker: Roger Mong (Pittsburgh Quantum Institute, USA)

  Title: Detecting topological order from modular transformations of ground states on the torus

  Bio: https://www.pqi.org/members/roger-mong

   

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• March 6, 2023 | Quantum Technology With Trapped IONS | Altaf Nizamani/Qirat Iqbal (University of Sindh, Pakistan)

  Quantum technology is a rapidly advancing field that is poised to revolutionize numerousindustries, including computing, communications, sensing, and cryptography. At its core, quantum technology relies on the principles of quantum mechanics, which allow for the creation of devices that operate on the quantum level. These devices based on quantum technology can perform tasks that are impossible or prohibitively difficult for classical devices. One of the most promisingapplications of quantum technology is in quantum computing, quantum communications, andquantum sensors.

  Trapped ions are one of the promising platform for quantum computing and sensing. In thisapproach, individual ions are trapped in a vacuum chamber using electromagnetic fields andmanipulated using lasers to perform quantum operations. As a quantum system, trapped ions offerseveral advantages. First, they have long coherence times, meaning that the quantum state of the ion can be preserved for a longer period, allowing for more complex calculations. Second, trapped ions can be precisely controlled and manipulated, allowing for the implementation of high-fidelity quantum gates. Finally, trapped ions can be entangled with one another, allowing for the implementation of quantum algorithms that are impossible to simulate on classical computers. Trapped ions also have great potential as quantum sensors. By using the properties of the ions to measure changes in their environment, trapped ions can detect minute changes in temperature, magnetic fields, and electric fields, among other things. This makes them useful for applications in precision measurement, such as in atomic clocks, gravitational wave detection, and magnetometry.

  One of the major challenges facing trapped ion systems is scalability. While individual ions have been used to perform simple quantum algorithms, scaling the system up to include a large number of ions is a difficult task. However, recent advances in ion trap technology have made it possible to trap larger numbers of ions and transport them in 2D and 3D space to perform more complex operations for quantum computation and sensing experiments. Realization of such devices is not far away. As compared to present atomic clocks, a new generation of quantum-enhanced clocks is now emerging showing significantly improved accuracy. Sensitive physical measurements are an essential component of modern science and technology. Developments in quantum sensors will outdate their classical counterparts.

  We will present recent developments and opportunities in quantum technology applications based on trapped ions, including quantum computation and sensing.

  Speakers: Altaf Nizamani and Qirat Iqbal.  (University of Sindh, Pakistan)

  Bio: https://usindh.edu.pk/portfolio/dr-altaf-hussain-nizamani/

  https://www.linkedin.com/in/qirat-iqbal-88a1251bb/?originalSubdomain=pk

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• February 27, 2023 | Quantum Computation: A Paradigm Shift | Aeysha Khalique (National University of Science and Technology, Pakistan)

  Quantum Mechanics offers such phenomena which defy our everyday observation. These are not just theoretical principles but have wide range applications in quantum computation and quantum information, making some tasks possible which are impossible to be done classically. This talk will take you to the journey through quantum computation, starting from underlying principles to the applications, including my own own contribution to it.

  Speaker: Aeysha Khalique (National University of Science and Technology, Pakistan)

  Bio: https://sns.nust.edu.pk/faculty/aeysha-khalique/

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• February 20, 2023 | Constructive Real Numbers in the Agda Proof Assistant | Zachary Murray (Dalhousie University, Canada)

  Proof assistant software enables the development of proofs in a manner such that a computer can verify their validity. As proof assistants commonly take the form of a programming language, users face programming-related problems, such as the naturality of expressing ideas and algorithms in the language, usability, and performance. We will investigate these issues as they occur in developing Errett Bishop’s constructive real numbers in the Agda proof assistant and functional programming language, with an introduction to each.

  Speaker: Zachary Murray (Dalhousie University, Canada)

  Bio: https://www.linkedin.com/in/zachary-murray-dal/?originalSubdomain=ca

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• February 13, 2023 | Demonstration of Quantum Energy Teleportation by Superconducting Quantum Processors and Implications for Communications and High Energy Physics | Kazuki Ikeda (Co-design Center for Quantum Advantage, Stony Brook University)

  Quantum energy teleportation is a theoretical concept in quantum physics thatdescribes the transfer of energy from one location to another without the need for a physical medium to carry it. This is made possible by means of universal properties of quantum entanglement and measurement of quantum states.

  The role of QET in physics and information engineering is largely unexplored, as the theory has not received much attention for long time since it was proposed about 15 years ago. To validate it on a real quantum processor, my research has tested the energy teleportation protocol in its most visible form for the first time on IBM's superconducting quantum computer. In my colloquium talk, I will explain the historical background of quantum energy teleportation, quantum circuits and quantum operations. Moreover I will present a concrete setup for a long-distance and large-scale quantum energy teleportation with real quantum networks.

  In addition, I will present the results of quantum simulations with relativistic field theory as a study based on the high-energy physics perspective and the symmetry-protected topological (SPT) phase of matter of quantum energy teleportation. The models will describe include the two dimensional QED (the massive Thirring model), the AKLT model, the Haldane model, and the Kitaev model. Those results show that the phase diagrams of the field theory and SPT phase are closely related to energy teleportation.

  In summary my talk will provide a novel suggestion that quantum energy teleportation paves a new pathway to a link between quantum communication on real quantum network, phase diagram of quantum many-body system, and quantum computation.

  Speaker: Kazuki Ikeda (Co-design Center for Quantum Advantage, Stony Brook University, USA)

  Bio: Kazuki Ikeda

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• 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: Vivek Singh

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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
  

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• 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)
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  Speaker: Tim Byrnes (NYUSH)