# Upcoming Seminars

Title: Counting Elliptic Curves Over Number Fields |
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Seminar: Algebra |

Speaker: Tristan Phillips of The University of Arizona |

Contact: David Zureick-Brown, david.zureick-brown@emory.edu |

Date: 2022-09-27 at 4:00PM |

Venue: MSC N304 |

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Abstract:Let $E$ be an elliptic curve over a number field $K$. The Mordell--Weil Theorem states that the set of rational points $E(K)$ of $E$ forms a finitely generated abelian group. In particular, we may write $E(K) = E(K)_{tors}\oplus \mathbb{Z}^r$, where $E(K)_{tors}$ is a finite torsion group, called the torsion subgroup of $E$, and $r$ is a non-negative integer, called the rank of $E$. In this talk I will discuss some results regarding how frequently elliptic curves with a prescribed torsion subgroup occur, and how one can bound the average analytic rank of elliptic curves over number fields. One of the main ideas behind these results is to use methods from Diophantine geometry to count points of bounded height on modular curves. |

Title: About the Lp theory for the non-cutoff Boltzmann equation |
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Seminar: Analysis and Differential Geometry |

Speaker: Ricardo Alonso of Texas A$\&$M at Qatar |

Contact: Maja Taskovic, maja.taskovic@emory.edu |

Date: 2022-09-29 at 4:00PM |

Venue: MSC W301 |

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Abstract:In this talk we discuss different technical elements to obtain a priori estimates for Lp norms of weak solutions to non-cutoff kinetic equations using as example the homogeneous/inhomogeneous Boltzmann equation. Rather than a detailed-proof talk, we point out difficulties and give some intuition related to the main steps of the strategy. In particular, we discuss the localization process of Boltzmann type operators which cover an ample range of operators such as the fractional Laplacian. |

Title: TBA |
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Seminar: Algebra |

Speaker: David Stapleton of The University of Michigan |

Contact: David Zureick-Brown, david.zureick-brown@emory.edu |

Date: 2022-10-04 at 4:00PM |

Venue: MSC N304 |

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Abstract: |

Title: Patch Normalizing Regularizer: Reconstruction using only one ground truth image |
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Seminar: Computational and Data Enabled Science |

Speaker: Paul Hagemann of TU Berlin |

Contact: Lars Ruthotto, lruthotto@emory.edu |

Date: 2022-10-06 at 10:00AM |

Venue: MSC W301 |

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Abstract:Reconstructing images from measurements (e.g. sinograms in CT) is a very active research topic. However in many domains, such as medical or material sciences, ground truth data is very hard or costly to obtain. In this talk, we will leverage the idea of patch-based learning for reconstructing images. The regularizer will learn the patch distribution from very few ground truth images by randomly subsampling 6x6 patches and learning their distribution. More specifically, we will use a normalizing flow to learn the patch distribution of the ground truth image, which we call patchNR. In reconstruction, we will minimize a sum of the negative log likelihood of the patches and the data fidelity term. Our method will be compared to other regularization techniques which use little data for CT, material and texture images. Furthermore, an outlook on how our method can be leveraged to perform zero shot superresolution will be given. |

Title: Complexities of the Cytoskeleton: Integration of Scales |
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Seminar: Computational and Data Enabled Science |

Speaker: Keisha Cook of Clemson University |

Contact: Jim Nagy, jnagy@emory.edu |

Date: 2022-10-07 at 1:00PM |

Venue: MSC W301 |

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Abstract:Biological systems are traditionally studied as isolated processes (e.g. regulatory pathways, motor protein dynamics, transport of organelles, etc.). Although more recent approaches have been developed to study whole cell dynamics, integrating knowledge across biological levels remains largely unexplored. In experimental processes, we assume that the state of the system is unknown until we sample it. Many scales are necessary to quantify the dynamics of different processes. These may include a magnitude of measurements, multiple detection intensities, or variation in the magnitude of observations. The interconnection between scales, where events happening at one scale are directly influencing events occurring at other scales, can be accomplished using mathematical tools for integration to connect and predict complex biological outcomes. In this work we focus on building inference methods to study the complexity of the cytoskeleton from one scale to another. |

Title: TBA |
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Seminar: Algebra |

Speaker: Brandon Alberts of Eastern Michigan University |

Contact: David Zureick-Brown, david.zureick-brown@emory.edu |

Date: 2022-10-14 at 4:00PM |

Venue: MSC W301 |

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Abstract: |

Title: TBA |
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Seminar: Algebra |

Speaker: Soumya Sankar of The Ohio State University |

Contact: David Zureick-Brwon, david.zureick-brown@emory.edu |

Date: 2022-10-14 at 5:15PM |

Venue: MSC W301 |

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Abstract: |

Title: Subspace configurations and low degree points on curves |
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Seminar: Algebra |

Speaker: Borys Kadets of University of Georgia |

Contact: David Zureick-Brown, david.zureick-brown@emory.edu |

Date: 2022-10-18 at 4:00PM |

Venue: MSC N304 |

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Abstract:The hyperelliptic curve given by the equation $y^2=f(x)$ with coefficients in $\mathbf{Q}$ has an unusual arithmetic property: it admits infinitely many points with coordinates in quadratic extensions of $\mathbf{Q}$ (namely $(a, \sqrt{f(a)})$). Hindry, motivated by arithmetic questions about modular curves, asked if the only curves that possess infinite collections of quadratic points are hyperelliptic and bielliptic; this conjecture was confirmed by Harris and Silverman. I will talk about the general problem of classifying curves that possess infinite collections of degree $d$ points. I will explain how to reduce this classification problem to a study of curves of low genus, and use this reduction to obtain a classification for $d \leq 5$. This relies on analyzing a discrete-geometric object -- the subspace configuration -- attached to curves with infinitely many degree $d$ points. This talk is based on joint work with Isabel Vogt (arXiv:2208.01067). |

Title: TBA |
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Seminar: Algebra |

Speaker: Daniel Keliher of University of Georgia |

Contact: David Zureick-Brown, david.zureick-brown@emory.edu |

Date: 2022-11-01 at 4:00PM |

Venue: MSC N304 |

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Abstract: |

Title: Athens-Atlanta joint Number Theory Seminar |
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Seminar: Algebra |

Speaker: Alina Bucur and Samit Dasgupta of USCD and Duke |

Contact: David Zureick-Brown, david.zureick-brown@emory.edu |

Date: 2022-11-07 at 4:00PM |

Venue: MSC W301 |

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Abstract: |