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August  August  August  1  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: Naturalness and muon anomalous magnetic moment
10:10 AM11:40 AM September 1, 2021 We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g2) are vectorlike singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimensionsix operator for (g−2) vanishes at oneloop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimensioneight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the viable parameter can be probed by the LHC and planned future colliders. https://harvard.zoom.us/j/977347126
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5  6  7  8  NUMBER THEORY SEMINAR
3:00 PM4:00 PM September 8, 2021 1 Oxford Street, Cambridge, MA 02138 USA The ptorsion in the class group of a number field K is conjectured to be small: of size at most Disc K^epsilon, and to have constant average size in families with a given Galois closure group (when p doesn’t divide the order of the group). In general, the best upper bound we have is Disc K^{1/2+epsilon}, and previously the only two cases known with constant average were for 3torsion in quadratic fields (Davenport and Heilbronn, 1971) and 2torsion in nonGalois cubic fields (Bhargava, 2005). We prove that the 3torsion is constant on average for fields with Galois closure group any 2group with a transposition, including, e.g. quartic D_4 fields. We will discuss the main inputs into the proof with an eye towards giving an introduction to the tools in the area. This is joint work with Robert Lemke Oliver and Jiuya Wang.  OPEN NEIGHBORHOOD SEMINAR
4:30 PM5:30 PM September 8, 2021 1 Oxford Street, Cambridge, MA 02138 USA Interesting patterns of prime numbers can arise in recursively defined sequences (such as the Fibonacci sequence). For nonlinear recursions, there are intriguing connections with complex dynamics and the Mandelbrot set. This is just one of the many ways that Number Theory and Chaotic Dynamical Systems come together. I’ll present a few examples and a glimpse into some of my own research in this direction.
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12  13  14  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR
10:30 AM12:00 PM September 14, 2021 Calabi–Yau manifolds of a given dimension are connected by an intricate web of birational maps. This web has deep consequences for the derived categories of coherent sheaves on such manifolds, and for the associated string theories. In particular, for 4folds and beyond, I will highlight certain simplices appearing in the web, and identify corresponding derived category structures. https://harvard.zoom.us/j/98781914555?pwd=bmVzZGdlRThyUDREMExab20ybmg1Zz09  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR
3:00 PM4:00 PM September 14, 2021 1 Oxford Street, Cambridge, MA 02138 USA The classical question of determining which varieties are rational has led to a huge amount of interest and activity. On the other hand, one can take on a complementary perspective: Given a smooth projective variety whose nonrationality is known, how far is it from being rational? I will explain recent progress in this direction for complete intersections in projective space.
 15  CMSA EVENT: CMSA Colloquium: Hyperbolic Geometry and Quantum Invariants
9:30 AM10:30 AM September 15, 2021 There are two very different approaches to 3dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship. Zoom link: https://harvard.zoom.us/j/95767170359?pwd=S0RheFJyMklwall1YnRKN2twcGxxdz09  CMSA EVENT: CMSA Joint Strongly Correlated/HighTc SC: Threeparticle mechanism for pairing and superconductivity
10:30 AM12:00 PM September 15, 2021 I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This threeparticle pairing mechanism leads to a variety of novel phenomena at finite doping, including spintriplet superconductivity, pair density wave, BCSBEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed. [1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021) [2] V. Crepel and L. Fu, arXiv:2103.12060 [3] K. Slagle and L. Fu, Phys. Rev. B 102, 235423 (2020) https://harvard.zoom.us/j/977347126  NUMBER THEORY SEMINAR
3:00 PM4:00 PM September 15, 2021 1 Oxford Street, Cambridge, MA 02138 USA We discuss the problem of determining the number of generators and relations of several profinite groups of arithmetic and geometric origin. These include etale fundamental groups of smooth projective varieties, absolute Galois groups of local fields, and Galois groups of maximal unramified extensions of number fields. The results are based on a cohomological presentability criterion of Lubotzky, and draw inspiration from wellknown facts about threedimensional manifolds, as in arithmetic topology. The talk is based on a joint work with Esnault and Srinivas, on a joint work with Jarden, and on work of Yuan Liu.  CMSA EVENT: CMSA New Technologies in Mathematics Seminar: Why abstraction is the key to intelligence, and what we’re still missing
3:00 PM4:00 PM September 15, 2021 This talk provides a personal perspective on the way forward towards more humanlike and more intelligent artificial systems. Traditionally, symbolic and probabilistic methods have dominated the domains of concept formation, abstraction, and automated reasoning. More recently, deep learningbased approaches have led to significant breakthroughs, including successes in games and combinatorial search tasks. However, the resulting systems are still limited in scope and capabilities — they remain brittle, datahungry, and their generalization capabilities are limited. We will address a set of questions: why is conceptual abstraction essential for intelligence? What is the nature of abstraction, and its relationship to generalization? What kind of abstraction can deep learning models generate, and where do they fail? What are the methods that are currently successful in generating strong conceptual abstraction? Finally, we will consider how to leverage a hybrid approach to reinforce the strength of different approaches while compensating for their respective weaknesses. *Special time – normally will be at 2 pm* https://harvard.zoom.us/j/99651364593?pwd=Q1R0RTMrZ2NZQjg1U1ZOaUYzSE02QT09
 16  CMSA EVENT: CMSA Quantum Matter in Mathematics & Physics Seminar: The Hilbert Space of large N ChernSimons matter theories
10:30 AM12:00 PM September 16, 2021 We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular, implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit; the final partition function reduces to a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics. https://harvard.zoom.us/j/977347126  CMSA EVENT: CMSA Active Matter Seminar: The many phases of a cell
1:00 PM2:00 PM September 16, 2021 I will begin by introducing an emerging paradigm of cellular organization – the dynamic compartmentalization of biochemical pathways and molecules by phase separation into distinct and multiphase condensates. Motivated by this, I will discuss two largely orthogonal problems, united by the theme of phase separation in multicomponent and chemically active fluid mixtures. 1. I will propose a theoretical model based on RandomMatrix Theory, validated by phasefield simulations, to characterizes the rich emergent dynamics, compositions, and steadystate properties that underlie multiphase coexistence in fluid mixtures with many randomly interacting components. 2. Motivated by puzzles in generegulation and nuclear organization, I will propose a role for how liquidlike nuclear condensates can be organized and regulated by the active process of RNA synthesis (transcription) and RNAprotein coacervation. Here, I will describe theory and simulations based on a Landau formalism and recent experimental results from collaborators.
 17  CMSA EVENT: CMSA Quantum Matter in Mathematics & Physics Seminar: Strong Coupling Theory of MagicAngle Graphene: A Pedagogical Introduction
3:30 PM5:00 PM September 17, 2021 In this talk, I will review a recently developed strong coupling theory of magicangle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigmamodel in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective superexchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform. —– Subscribe to Harvard CMSA seminar videos (more to be uploaded): https://www.youtube.com/channel/UCBmPOOK1sa8T1oX_9aVhAg/playlists https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww https://harvard.zoom.us/j/977347126
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19  20  21  CMSA EVENT: CMSA Combinatorics, Physics and Probability Seminar: Surfacehedra and the Binary Positive Geometry of Particle and “String” Amplitudes
9:30 AM10:30 AM September 21, 2021  CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: What do bounding chains look like, and why are they related to linking numbers?
10:30 AM11:30 AM September 21, 2021 GromovWitten invariants count pseudoholomorphic curves on a symplectic manifold passing through some fixed points and submanifolds. Similarly, open GromovWitten invariants are supposed to count disks with boundary on a Lagrangian, but in most cases such counts are not independent of some choices as we would wish. Motivated by Fukaya’11, J. Solomon and S. Tukachinsky constructed open GromovWitten invariants in their 2016 papers from an algebraic perspective of $A_{\infty}$algebras of differential forms, utilizing the idea of bounding chains in FukayaOhOhtaOno’06. On the other hand, Welschinger defined open invariants on sixfolds in 2012 that count multidisks weighted by the linking numbers between their boundaries. We present a geometric translation of SolomonTukachinsky’s construction. From this geometric perspective, their invariants readily reduce to Welschinger’s. https://harvard.zoom.us/j/98781914555?pwd=bmVzZGdlRThyUDREMExab20ybmg1Zz09  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR
3:00 PM4:00 PM September 21, 2021 1 Oxford Street, Cambridge, MA 02138 USA Algebraic geometry has furnished fruitful tools for studying matroids, which are combinatorial abstractions of hyperplane arrangements. We first survey some recent developments, pointing out how these developments remained partially disjoint. We then introduce certain vector bundles (Kclasses) on permutohedral varieties, which we call “tautological bundles (classes)” of matroids, as a new framework that unifies, recovers, and extends these recent developments. Our framework leads to new questions that further probe the boundary between combinatorics and geometry. Joint work with Andrew Berget, Hunter Spink, and Dennis Tseng.
 22  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: Symmetry types in QFT and the CRT theorem
10:30 AM12:00 PM September 22, 2021 I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation. I will then indicate how thebasic CRT theorem works for general symmetry types, focusing on the case of the pin groups. In particular, I expand on a subtlety first flagged by GreavesThomas. https://harvard.zoom.us/j/977347126  NUMBER THEORY SEMINAR
3:00 PM4:00 PM September 22, 2021 1 Oxford Street, Cambridge, MA 02138 USA Given a variety over a number field, its geometric etale fundamental group comes equipped with an action of the Galois group. This induces a Galois action on the proalgebraic completion of the etale fundamental group and hence the ring of functions on that proalgebraic completion provides a supply of Galois representations. It turns out that any finitedimensional padic Galois representation contained in the ring of functions on the proalgebraic completion of the fundamental group of a smooth variety satisfies the assumptions of the FontaineMazur conjecture: it is de Rham at places above p and is a. e. unramified. Conversely, we will show that every semisimple representation of the Galois group of a number field coming from algebraic geometry (that is, appearing as a subquotient of the etale cohomology of an algebraic variety) can be established as a subquotient of the ring of functions on the proalgebraic completion of the fundamental group of the projective line with 3 punctures.  OPEN NEIGHBORHOOD SEMINAR
4:30 PM5:30 PM September 22, 2021 1 Oxford Street, Cambridge, MA 02138 USA Projective space and complex tori are two of the simplest types of manifolds we encounter, and in many ways they seem very different from each other. I will try to convince you however that, at least if we consider a special (but at the same time very common) class of tori called principally polarized abelian varieties, then the geometry of their subvarieties exhibits surprising, and to date mostly unexplained, similarities to the geometry of subvarieties in projective space.
 23  CMSA EVENT: CMSA Interdisciplinary Science Seminar: The number of nqueens configurations
9:00 AM10:00 AM September 23, 2021 The nqueens problem is to determine Q(n), the number of ways to place n mutually nonthreatening queens on an n x n board. The problem has a storied history and was studied by such eminent mathematicians as Gauss and Polya. The problem has also found applications in fields such as algorithm design and circuit development. Despite much study, until recently very little was known regarding the asymptotics of Q(n). We apply modern methods from probabilistic combinatorics to reduce understanding Q(n) to the study of a particular infinitedimensional convex optimization problem. The chief implication is that (in an appropriate sense) for a~1.94, Q(n) is approximately (ne^(a))^n. Furthermore, our methods allow us to study the typical “shape” of nqueens configurations. Zoom ID: 950 2372 5230 (Password: cmsa)  CMSA EVENT: CMSA Quantum Matter in Mathematics & Physics Seminar: Applications of instantons, sphalerons and instantondyons in QCD
10:30 AM12:00 PM September 23, 2021 I start with a general map of gauge topology, including monopoles, instantons and instantondyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of ChernSimons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instantonantiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC. Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spindependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instantondyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD. https://harvard.zoom.us/j/977347126 Password: cmsa  CMSA EVENT: CMSA Active Matter Seminar: The many phases of a cell
1:00 PM2:00 PM September 23, 2021 I will begin by introducing an emerging paradigm of cellular organization – the dynamic compartmentalization of biochemical pathways and molecules by phase separation into distinct and multiphase condensates. Motivated by this, I will discuss two largely orthogonal problems, united by the theme of phase separation in multicomponent and chemically active fluid mixtures. 1. I will propose a theoretical model based on RandomMatrix Theory, validated by phasefield simulations, to characterizes the rich emergent dynamics, compositions, and steadystate properties that underlie multiphase coexistence in fluid mixtures with many randomly interacting components. 2. Motivated by puzzles in generegulation and nuclear organization, I will propose a role for how liquidlike nuclear condensates can be organized and regulated by the active process of RNA synthesis (transcription) and RNAprotein coacervation. Here, I will describe theory and simulations based on a Landau formalism and recent experimental results from collaborators. *rescheduled from 9/16/21  ALGEBRAIC DYNAMICS SEMINAR
4:00 PM6:00 PM September 23, 2021 Given a rational map defined over a number field, the Galois orbits of points with canonical height tending to zero will equidistribute to a measure supported on the Julia set. If one is able to extend the space of test functions to include those with certain logarithmic poles, then it is possible to obtain finiteness results on Sintegral points. In this talk, we will study quantitative versions of logarithmic equidistribution in some special situations and their implications. http://people.math.harvard.edu/~demarco/AlgebraicDynamics/
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26  27  28  CMSA EVENT: CMSA Combinatorics, Physics and Probability Seminar: The hypersimplex and the m=2 amplituhedron
9:30 AM10:30 AM September 28, 2021
I’ll discuss a curious correspondence between the m=2 amplituhedron, a 2kdimensional subset of Gr(k, k+2), and the hypersimplex, an (n1)dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map, respectively), but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). Along the way, we prove the signflip description of the m=2 amplituhedron conjectured by ArkaniHamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Euleriannumbermany chambers (inspired by an analogous hypersimplex decomposition).
https://harvard.zoom.us/j/94191911494?pwd=RnN3ZnIwcFYwd0QyT0MwZWVISmR5Zz09 Password: 1251442  CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: The Mirror ClemensSchmid Sequence
10:30 AM11:30 AM September 28, 2021 I will present a fourterm exact sequence relating the cohomology of a fibration to the cohomology of an open set obtained by removing the preimage of a general linear section of the base. This exact sequence respects three filtrations, the Hodge, weight, and perverse Leray filtrations, so that it is an exact sequence of mixed Hodge structures on the graded pieces of the perverse Leray filtration. I claim that this sequence should be thought of as a mirror to the ClemensSchmid sequence describing the structure of a degeneration and formulate a “mirror P=W” conjecture relating the filtrations on each side. Finally, I will present evidence for this conjecture coming from the K3 surface setting. This is joint work with Charles F. Doran. https://harvard.zoom.us/j/98781914555?pwd=bmVzZGdlRThyUDREMExab20ybmg1Zz09
 29  CMSA EVENT: CMSA Colloquium: Langlands duality for 3 manifolds
9:30 AM10:30 AM September 29, 2021
Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4dimensional super symmetric quantum field theory by Kapustin and Witten. However to this day the Hilbert space attached to 3manifolds, and hence the precise form of Langlands duality for them, remains a mystery. In this talk I will propose that socalled “skein modules” of 3manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with BenZvi, Gunningham and Safronov. Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.  CMSA EVENT: CMSA JOINT QUANTUM MATTER IN MATH & PHYSICS and STRONGLY CORRELATED QUANTUM MATERIALS & HIGHTEMPERATURE SUPERCONDUCTORS SEMINAR: Oscillations in the thermal conductivity of a spin liquid*
11:30 AM1:00 PM September 29, 2021
The layered honeycomb magnet alphaRuCl3 orders below 7 K in a zigzag phase in zero field. An inplane magnetic field Ha suppresses the zigzag order at 7 Tesla, leaving a spindisordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a breakinslope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent halfquantization results. *Czajka et al., Nature Physics 17, 915 (2021). Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.
https://harvard.zoom.us/j/977347126 Password: cmsa  NUMBER THEORY SEMINAR
3:00 PM4:00 PM September 29, 2021 1 Oxford Street, Cambridge, MA 02138 USA
I will explain a conjecture on density of arithmetic Hodge loci which includes and generalizes several recent density results of these loci in arithmetic geometry. This conjecture has also analogues over functions fields that I will survey. As a particular instance, I will outline the proof of the following result: a K3 surface over a number field admits infinitely many specializations where its Picard rank jumps. This last result is joint work with Ananth Shankar, Arul Shankar and Yunqing Tang.
 30  CMSA EVENT: CMSA Active Matter Seminar: Cytoskeletal Energetics and Energy Metabolism
1:00 PM2:00 PM September 30, 2021 Life is a nonequilibrium phenomenon. Metabolism provides a continuous flux of energy that dictates the form and function of many subcellular structures. These subcellular structures are active materials, composed of molecules which use chemical energy to perform mechanical work and locally violate detailed balance. One of the most dramatic examples of such a selforganizing structure is the spindle, the cytoskeletal based assembly which segregates chromosomes during cell division. Despite its central role, very little is known about the nonequilibrium thermodynamics of active subcellular matter, such as the spindle. In this talk, I will describe ongoing work from my lab aimed at understanding the flows of energy which drive the nonequilibrium behaviors of the cytoskeleton in vitro and in vivo. *rescheduled from 9/16/21  COLLOQUIUMS
4:30 PM5:30 PM September 30, 2021 1 Oxford Street, Cambridge, MA 02138 The field of Geometric Set Theory studies structures on sets of countable objects (typically Polish spaces) by considering virtual objects, typically uncountable sets representing members of the space under consideration in some larger model of set theory. This approach can be used to study analytic equivalence relations on Polish spaces, where the virtual objects represent equivalence classes. The representatives of the virtual classes can be used for instance to prove nonreducibility results between such equivalence relations. Another set of applications involves separating forms of the Axiom of Choice, specifically forms asserting the existence of a set of reals with certain first order properties. Typical examples include Vitali sets, Hamel bases, discontinuous homomorphisms on the real line or countable colorings of various graphs on Euclidean space. We will give a brief tour of some of the landmarks in the area, and discuss some directions for further research.
 October  October 