The Quadratic Formula Revisited
Bernd Strumfels Max Planck Institute for Mathematics in the Sciences
85 - 96 of 19186 Results
Format results
Axion-dilaton interactions in the dark sector
Adam Smith University of Sheffield
String Theory Course Q&A
PIRSA:25050007Neural Networks and Quantum Mechanics
Christian Ferko Northeastern University
Improving prospects for the direct detection of Higgsino dark matter
Harikrishnan Ramani University of Delaware
Quantum Gravity and Effective Topology
Renate Loll Radboud Universiteit Nijmegen
2-dimensional topological field theories via the genus filtration
Jan SteinebrunnerQuantum Chemistry in the Universe’s Coldest Test Tube
Alan Jamison Institute for Quantum Computing (IQC)
PIRSA:25050015
The Quadratic Formula Revisited
Bernd Strumfels Max Planck Institute for Mathematics in the Sciences
High school students learn how to express the solution of a quadratic equation in one unknown in terms of its three coefficients. Why does this formula matter? We offer an answer in terms of discriminants and data. This lecture invites the audience to a journey towards non-linear algebra.
Approximate entropy accumulation
Frédéric DupuisThe entropy accumulation theorem (EAT) allows us to lower bound the min-entropy of a state that can be generated by a chain of quantum channels satisfying a Markov chain condition, and can be used to prove the security of QKD protocols, including device-independent ones. However, one of its drawbacks is that it only applies to states with a fairly rigid structure; in particular, the Markov chain condition must be satisfied exactly. What happens when we relax this assumption by allowing the required structure to be satisfies only approximately? Does doing so lead to interesting applications? We answer both questions by the affirmative: we present two flavours of approximate EAT, and show that it can be used to prove the security of parallel device-independent QKD, and to analyze QKD protocols under source correlations. Along the way, we will introduce the concept of "approximation chain" which underpins the new results. This is joint work with Ashutosh Marwah; the talk will cover material from 2412.06723, 2402.12346, and 2308.11736.Axion-dilaton interactions in the dark sector
Adam Smith University of Sheffield
Axion-dilaton models provide a well-motivated, minimal class of models for which kinetic interactions between multiple scalar fields and their predictions can be explored, in particular in late time cosmology. I will review this class of models and present the formalism we developed for studying kinetic interactions between rapidly oscillating axion fields and their dilaton partners on cosmological scales.Self testing in General Probabilistic Theories
Lionel DmelloThis talk will consist of two parts. In the former I discuss published work [LD, Ligthart, Gross, PRA, 2024], and in the latter some new related results. Part 1 -- Although there exist theories with "stronger bipartite entanglement" than quantum mechanics (QM), in sense that they have a larger CHSH value than Tsirelson's bound for QM, all such theories known tend to come at a cost, namely, they have strictly weaker bipartite measurements. Thus it has been conjectured that if one looks at scenarios where the correlations depend both on bipartite states and bipartite measurements, e.g. entanglement swapping, such theories cannot beat QM. However, in our recent work [LD, Ligthart, Gross, PRA, 2024], we constructed a General Probabilistic Theory (GPT) -- Oblate Stabilizer Theory (OST) -- that can both achieve a CHSH value of 4 (the mathematical maximum), and maintain this CHSH value after arbitrarily many rounds of entanglement swapping, effectively ruling out this conjecture. Part 2 -- One particularly non-intuitive feature of OST (for those in the know) is the presence of a "spurious extra dimension" in the local theory: Even though the CHSH violation involves only a two-dimensional section of local state space, we failed to make the entanglement swapping property work without going to three dimensions. In ongoing work, we managed to identify the mechanism behind this phenomenon. To this end, we have introduced a notion of self-testing for GPTs, and, using this we have established a GPT version of the "no-pancake" theorem that says that there is no completely positive map that maps the Bloch sphere to a two-dimensional section. Further, under reasonable assumptions, we have also managed to establish the uniqueness of OST, and provide a prescription for the construction of GPTs capable of stable iterated entanglement swapping.String Theory Course Q&A
PIRSA:25050007Neural Networks and Quantum Mechanics
Christian Ferko Northeastern University
In this talk, I will survey recent developments about the connection between neural networks and models of quantum mechanics and quantum field theory. Previous work has shown that the neural network - Gaussian process correspondence can be interpreted as the statement that large-width neural networks share some properties with free, or weakly interacting, quantum field theories (QFTs). Here I will focus on 1d QFTs, or models of quantum mechanics, where one has greater theoretical control. For instance, under mild assumptions, one can prove that any model of a quantum particle admits a representation as a neural network. Cherished features of quantum mechanics, such as uncertainty relations, emerge from specific architectural choices that are made to satisfy the axioms of quantum theory. Based on 2504.05462 with Jim Halverson.
Improving prospects for the direct detection of Higgsino dark matter
Harikrishnan Ramani University of Delaware
The pseudo-Dirac Higgsino is one of the last surviving electroweak WIMPs. The LHC will not reach the 1.1 TeV target mass even with full luminosity and prospects for its indirect detection depend on a favorable dark matter density profile at the galactic center. Since it has only off-diagonal couplings at tree-level, its direct detection is possible only when the mass splitting is smaller than the initial center of mass kinetic energy. This direct detection loophole is actually more generic; going by the name 'inelastic dark matter'. In this talk I will talk about my recent efforts to reach mass splittings larger than what has been thought to be possible thus far, by invoking interesting astrophysics, elements from the end of the periodic table, and large volume neutrino detectors.
Quantum Gravity and Effective Topology
Renate Loll Radboud Universiteit Nijmegen
My presentation will introduce a new methodology to characterize properties of quantum spacetime in a strongly quantum-fluctuating regime, using tools from topological data analysis. Starting from a microscopic quantum geometry, generated nonperturbatively in terms of dynamical triangulations (DT), we compute the homology of a sequence of coarse-grained versions of the geometry as a function of the coarse-graining scale. This gives rise to a characteristic "topological finger print" of the quantum geometry. I discuss the results for Lorentzian and Euclidean 2D quantum gravity, defined via lattice quantum gravity based on causal and Euclidean DT. For the latter, our numerical analysis reproduces the well-known string susceptibility exponent governing the scaling behaviour of the partition function. [Joint work with Jesse van der Duin, Marc Schiffer and Agustin Silva, to appear.]2-dimensional topological field theories via the genus filtration
Jan SteinebrunnerBy a folk theorem (non-extended) 2-dimensional TFTs valued in the category of vector spaces are equivalent to commutative Frobenius algebras. Upgrading the bordism category to an (infinity, 1)-category whose 2-morphism are diffeomorphisms, one can study 2D TFTs valued in higher categories, leading for example to (derived) modular functors and cohomological field theories. I will explain how to describe such more general (non-extended) 2D TFTs as algebras over the modular infinity-operad of surfaces. In genus 0 this yields an E_2^{SO}-Frobenius algebra and I will outline an obstruction theory for inductively extending such algebras to higher genus. Specialising to invertible TFTs, this amounts to a genus filtration of the classifying space of the bordism category and hence the Madsen--Tillmann spectrum MTSO_2. The aforementioned obstruction theory identifies the associated graded in terms of curve complexes and thereby yields a spectral sequence starting with the unstable and converging to the stable cohomology of mapping class groups.Quantum Chemistry in the Universe’s Coldest Test Tube
Alan Jamison Institute for Quantum Computing (IQC)
PIRSA:25050015Abstract
How do chemical reactions change when they’re run at temperatures a billion times colder than a Canadian winter? What can we learn when we have perfect quantum control of the reactants? Before answering these questions, we’ll discuss the fascinating techniques of laser cooling that allow us to cool atoms and molecules to within a few billionths of a degree above absolute zero. We’ll then look at how molecules prepared at such temperatures allow us to control chemical reactions at the quantum level, beginning to open a new understanding of chemistry and new possibilities for technologies of the future.
About the Speaker
Dr. Alan Jamison is an Assistant Professor at the University of Waterloo, jointly appointed to the Department of Physics and Astronomy and the Institute for Quantum Computing (IQC). He leads the Jamison Lab, which investigates ultracold atoms and molecules to explore quantum many-body physics, quantum chemistry, and quantum information science. Dr. Jamison earned his B.S. in Mathematics from the University of Central Florida in 2007, followed by an M.S. and Ph.D. in Physics from the University of Washington in 2008 and 2014, respectively.
After completing his Ph.D., he joined the group of Nobel Laureate Wolfgang Ketterle at the Massachusetts Institute of Technology (MIT) as a postdoctoral researcher. At the University of Waterloo, Dr. Jamison's research centers on using ultracold atoms and molecules to investigate complex quantum systems. His lab aims to achieve precise control over chemical reactions at ultracold temperatures, providing insights into quantum chemistry and enabling advancements in quantum computing and simulation.
Supporting neurodivergence and understanding neurodivergent ways of being (brought to PI by the Mental Health Working Group)
Helen HargreavesHelen Hargreaves, MSW, RSW will present a workshop for PI Residents, providing information on the basics of Emotion Theory, how to assess ones own needs and communicate them. This presentation will particularly focus on Autistic and other neurodivergent ways of experiencing emotions and stress and how to better support neurodivergent team members in the workplace. Helen Hargreaves is a Neurodivergent Therapist with over 15 years experience workings with Neurodivergent clients. She is the Director of Rainbow Brain, a social work group practice that focuses on providing queer, trans and neurodivergent affirming therapy. Please note that this will be a 1.5 hour session with presentation and experiential components.