Calendar
- 10April 10, 2022No events
- 11April 11, 2022No events
- 12April 12, 2022
CMSA Combinatorics, Physics and Probability Seminar: BCFW recursion relations and non-planar positive geometry
20 Garden Street, Cambridge, MA 02138There is a close connection between the scattering amplitudes in planar N=4 SYM theory and the cells in the positive Grassmannian. In the context of BCFW recursion relations the tree-level S-matrix is represented as a sum of planar on-shell diagrams (aka plabic graphs) and associated with logarithmic forms on the Grassmannian cells of certain dimensionality. In this talk, we explore non-adjacent BCFW shifts which naturally lead to non-planar on-shell diagrams and new interesting subspaces inside the real Grassmannian.
in person – CMSA, 20 Garden St, Room G10
via Zoom – register at: CMSA Combinatorics, Physics and Probability Seminar
Normal bundles of canonical curves
The extrinsic geometry of the canonical model of a nonhyperelliptic curve captures many aspects of the intrinsic geometry of the curve. In this talk I will discuss joint work with Izzet Coskun and Eric Larson in which we show that the normal bundle of a general canonical curve of genus at least 7 is always semistable. This makes substantial progress towards a conjecture of Aprodu–Farkas–Ortega, and answers it completely in a third of all cases.
- 13April 13, 2022
CMSA Colloquium: Quantisation in monoidal categories and quantum operads
The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S, compatible with this structure.But in fact, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops, – nonassociative analogs of groups.The idea of symmetry as a group is closely related to classical physics, in a very definite sense, going back at least to Archimedes. When quantum physics started to replace classical, it turned out that classical symmetries must also be replaced by their quantum versions, e.g. quantum groups.In this talk we explain how to define and study quantum versions of symmetries, relevant to information theory and other contexts.
For information on how to join, please see: https://cmsa.fas.harvard.edu/seminars-and-colloquium/
Euler systems and the p-adic Langlands correspondence
1 Oxford Street, Cambridge, MA 02138 USAAbout 2 years ago, I have given a new construction of the Euler system of cyclotomic units via Eisenstein congruences in which the p-adic Langlands correspondence for GL_2(\Q_p) plays a central role. In this talk, I want to explain how one can extend this method to obtain a large class of new Euler systems attached to ordinary automorphic forms. This is a work in progress.
CMSA Quantum Matter in Mathematics and Physics: Late time von Neumann entropy and measurement-induced phase transition
**Note special time**It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase.
We re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature.We then consider a simpler four-flavor axial gauge model, the 14(-1)4 model, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior.Finally, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.—–Subscribe to Harvard CMSA Quantum Matter and other seminar videos (more to be uploaded):Subscribe to Harvard CMSA seminar mailing list: https://forms.gle/
1ewa7KeP6BxBuBeRA For information on how to join, please see: https://cmsa.fas.harvard.edu/quantum-matter-seminar
- 14April 14, 2022
CMSA Interdisciplinary Science Seminar: SIMPLEs: a single-cell RNA sequencing imputation strategy preserving gene modules and cell clusters variation
A main challenge in analyzing single-cell RNA sequencing (scRNA-seq) data is to reduce technical variations yet retain cell heterogeneity. Due to low mRNAs content per cell and molecule losses during the experiment (called ‘dropout’), the gene expression matrix has a substantial amount of zero read counts. Existing imputation methods treat either each cell or each gene as independently and identically distributed, which oversimplifies the gene correlation and cell type structure. We propose a statistical model-based approach, called SIMPLEs (SIngle-cell RNA-seq iMPutation and celL clustErings), which iteratively identifies correlated gene modules and cell clusters and imputes dropouts customized for individual gene module and cell type. Simultaneously, it quantifies the uncertainty of imputation and cell clustering via multiple imputations. In simulations, SIMPLEs performed significantly better than prevailing scRNA-seq imputation methods according to various metrics. By applying SIMPLEs to several real datasets, we discovered gene modules that can further classify subtypes of cells. Our imputations successfully recovered the expression trends of marker genes in stem cell differentiation and can discover putative pathways regulating biological processes.For information on how to join, please go to: https://cmsa.fas.harvard.edu/interdisciplinary-science-seminar
CMSA Quantum Matter in Mathematics and Physics: Cancellation of the vacuum energy and Weyl anomaly in the standard model, and a two-sheeted, CPT-symmetric universe
I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields. Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, including right-handed neutrinos. Moreover, the scalars possess a scale-invariant power spectrum, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation).
As context, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role. Our universe seems to be dominated by radiation at early times, and positive vacuum energy at late times. Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets, related by a symmetry that, in turn, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime. This line of thought suggests new explanations for a number of observed properties of the universe, including: its homogeneity, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which, in this picture, is a right-handed neutrino, radiated from the early universe like Hawking radiation from a black hole). It also makes a number of testable predictions.
(Based on recent, and ongoing, work with Neil Turok: arXiv:1803.08928, arXiv:2109.06204, arXiv:2110.06258, arXiv:2201.07279.)
—–Subscribe to Harvard CMSA Quantum Matter and other seminar videos (more to be uploaded):Subscribe to Harvard CMSA seminar mailing list: https://forms.gle/
1ewa7KeP6BxBuBeRA For information on how to join, please see: https://cmsa.fas.harvard.edu/quantum-matter-seminar
Algebraic Dynamics: Dynamical cancellation
Let X be a projective variety and let f be a dominant endomorphism of f, both of which are defined over a number field K. We consider the question of when there is some integer n, depending only on X and K, such that whenever x and y are K-points of X with the property that some iterate of f maps x and y to the same point, we necessarily have that the n-th iterate of f also achieves this. We consider this an instance of “dynamical cancellation’’ and we show that such a cancellation result holds for etale morphisms of projective varieties as well as self-maps of smooth projective curves. As a result we are able to prove a general cancellation result for semigroups of polynomials: if f_1, … , f_r are polynomials of degree at least two then there is a proper closed subset of P^1 x P^1 with the property that for any a, b in K satisfying phi(a)=phi(b) for some phi in the semigroup generated by f_1, … f_r under composition, we necessarily have (a,b) lies in this closed subset. Moreover, we show that this Z can be taken to be the union of the diagonal with a finite set of points for “non-exceptional” semigroups. This is joint work with Matt Satriano and Yohsuke Matsusawa.
Go to http://people.math.harvard.
edu/~demarco/ AlgebraicDynamics/ for more information - 15April 15, 2022
Workshop on Machine Learning and Mathematical Conjecture
1 Oxford Street, Cambridge, MA 02138 USAOn April 15, 2022, the CMSA will hold a one-day workshop, Machine Learning and Mathematical Conjecture, related to the New Technologies in Mathematics Seminar Series. Organizers: Michael R. Douglas (CMSA/Stony Brook/IAIFI) and Peter Chin (CMSA/BU).
Machine learning has driven many exciting recent scientific advances. It has enabled progress on long-standing challenges such as protein folding, and it has helped mathematicians and mathematical physicists create new conjectures and theorems in knot theory, algebraic geometry, and representation theory.
At this workshop, we will bring together mathematicians, theoretical physicists and machine learning researchers to review the state of the art in machine learning, discuss how ML results can be used to inspire, test and refine precise conjectures, and identify mathematical questions which may be suitable for this approach.
Speakers:
James Halverson, Northeastern University Dept. of Physics and IAIFI
Fabian Ruehle, Northeastern University Dept. of Physics and Mathematics and IAIFI
Andrew Sutherland, MIT Department of Mathematics
9:30 am – 10:20 am James Halverson: Machine Learning for Mathematicians 10:30 am – 11:20 am Andrew Sutherland: Number Theory 11:30 am – 12:20 pm Fabian Ruehle: Knot Theory Lunch break 2:00 pm –3:30 pm Computer demonstrations 3:45 pm – 4:45 pm Discussion The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.
For a list of lodging options convenient to the Center, please visit our recommended lodgings page.All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival: https://forms.gle/xKykcNcXq7ciZuvJ8To attend, please REGISTER ONLINE.
- 16April 16, 2022No events