Maths anxiety is a well-defined cognitive, physiological, and psychological construct that negatively affects the maths achievement of students who suffer from it. Maths anxiety does not end when a student leaves school, and can negatively impact their adult life.

This talk will present an informal introduction into the study of maths anxiety and other related constructs that affect the learning of maths. Then a brief discussion of the use of history of mathematics in the classroom. The aim of this talk is to examine a case study investigating whether the history of mathematics can alleviate maths anxiety by developing a dialogical classroom in which success is measured not by solving equations quickly, but by engaging in discussion mathematically.

In this talk, I will consider the incompressible Navier-Stokesequations in the mild solution setting. Using this setting, I will show how to obtain analyticity of mild solutions using the Gevrey regularity technique. This regularity enables to get decay rates of weak solutions of the Navier-Stokes equations. This idea can be applied to other dissipative equations with analytic nonlinearities. I will finally consider the regularity of the flow map of mild solutions using the Log-Lipschitz regularity of the velocity field.

A mathematical analysis of Matt McDuff’s 2016 attempt to ride a world record
40 foot (12.3 meter) high vertical circular loop-de-loop he named ``The Loop of Doom''.

In this talk, I will discuss several results on determining the tower growth rate of Ramsey numbers arising in combinatorics and in geometry.

These results are joint work with David Conlon, Jacob Fox, Dhruv Mubayi, Janos Pach, and Benny Sudakov.

\indent Data science is at a crossroads. Each year, thousands of new data scientists are entering science and technology, after a broad training in a variety of fields. Modern data science is often exploratory in nature, with datasets being collected and dissected in an interactive manner. Classical guarantees that accompany many statistical methods are often invalidated by their non-standard interactive use, resulting in an underestimated risk of falsely discovering correlations or patterns. It is a pressing challenge to upgrade existing tools, or create new ones, that are robust to involving a human-in-the-loop.

In this talk, I will describe two new advances that enable some amount of interactivity while testing multiple hypotheses, and control the resulting selection bias. I will first introduce a new framework, STAR, that uses partial masking to divide the available information into two parts, one for selecting a set of potential discoveries, and the other for inference on the selected set. I will then show that it is possible to flip the traditional roles of the algorithm and the scientist, allowing the scientist to make post-hoc decisions after seeing the realization of an algorithm on the data. The theoretical basis for both advances is founded in the theory of martingales : in the first, the user defines the martingale and associated filtration interactively, and in the second, we move from optional stopping to optional spotting by proving uniform concentration bounds on relevant martingales.

Bio: Aaditya Ramdas is a postdoctoral researcher in Statistics and EECS at UC Berkeley, advised by Michael Jordan and Martin Wainwright. He finished his PhD in Statistics and Machine Learning at CMU, advised by Larry Wasserman and Aarti Singh, winning the Best Thesis Award in Statistics. A lot of his research focuses on modern aspects of reproducibility in science and technology — involving statistical testing and false discovery rate control in static and dynamic settings.

This talk will feature joint work with (alphabetically) Rina Barber, Jianbo Chen, Will Fithian, Kevin Jamieson, Michael Jordan, Eugene Katsevich, Lihua Lei, Max Rabinovich, Martin Wainwright, Fanny Yang and Tijana Zrnic.

et $E$ be an elliptic curve defined over a number field $k$ and $F$ a finite cyclic extension of $k$ of $p$-power
degree for an odd prime $p$.
Under certain technical hypotheses, we describe a reinterpretation of the Equivariant Tamagawa Number Conjecture
(`ETNC') for $E$, $F/k$ and $p$ as an explicit family of
$p$-adic congruences involving values of derivatives of the Hasse-Weil $L$-functions of twists of $E$,
normalised by completely explicit twisted regulators. This
reinterpretation makes the ETNC amenable to numerical verification and furthermore leads to explicit predictions
which refine well-known conjectures of Mazur and Tate.

This is a report on joint work with Daniel Macias Castillo

Modular forms, being some of the most
fundamental objects in number theory, have a habit of appearing in
many different contexts; such coincidences turn out to be extremely
useful for computational purposes. I'll describe three different
constructions that give the action of the Hecke operators on certain
spaces of modular forms: the classical method of modular symbols
(Manin), the``method of graphs'' based on isogenies among supersingular
elliptic curves (Mestre-Oestrele), and a less well-known method based
of reduction of quadratic forms (Birch).

We consider the problem of decomposing an even order symmetric tensor with positive eigenvalues, into a sum of rank-1 components (also knows as canonical polyadic or CP decomposition). These tensors naturally arise in many signal processing applications (such as ICA, blind source separation, source localization) when we compute higher order cumulants of the measurements. We show that when these components possess certain harmonic structures, it is possible to design clever sampling techniques to identify $O(N^{2q})$ rank-1 factors using a tensor of order $2q$ (where $q$ is an integer) and dimension $N$. This is made possible by exploiting the idea of a higher order difference set that can be associated with the cumulant tensors. For unstructured even order tensors, we show that under some mild conditions, the problem of CP decomposition is equivalent to solving a system of quadratic equations as long as the rank of the tensor is $O(N^q)$. We finally propose two algorithms, one based on convex relaxation, and the other utilizes non-convex, Jacobi iteration to solve the resulting quadratic system.

In this project, we assess the impact of granting farmers title to their land on agricultural productivity in Benin. We test the hypothesis that formalizing land tenure and land use rights raises the incentives to landholders for making sustainable investments in their productive operations. We use remote sensing data to measure annual patterns of vegetation over time and apply a difference-in-differences and staggered-entry estimation strategy to identify program treatment effects. To assess patterns of annual vegetation cover across Benin, we use satellite observations of land cover from Landsat 7 to generate spectral indices that are sensitive to live vegetation and the presence of water (e.g., NDVI, SAVI, EVI, NDWI, and LSWI). To detect seasonal changes in vegetation, we analyze indices at high temporal resolution and fit sinusoids to the data. We perform the analysis at three geographical scales: the level of the village, the level of the plot, and the level of the
pixel. For the pixel-level analysis, we sample a large number of pixels within villages, and calculate and analyze temporal changes in the per-pixel spectral indices over the period 2005 to 2015. For the analysis at the village level, we aggregate the pixels spatially to the level of the village, and analyze a full time series of both means and variances at the village scale. We compare results across spatial scales (pixel, plot, village) to understand the relative importance of spatial and temporal degrees of freedom in detecting land investments.

Markov duality in spin chains and exclusion processes has found a wide variety of applications throughout probability theory. We review the duality of the asymmetric simple exclusion process (ASEP) and its underlying algebraic symmetry. We then explain how the algebraic structure leads to a wide generalization of models with duality, such as higher spin exclusion processes, zero range processes, stochastic vertex models, and their multi-species analogues.

This is a continuation of my RTG colloquium lecture on November 8. In this lecture, we study the method of Birch in more detail, to see how it can be used to compute essentially arbitrary spaces of classical modular forms. This involves relating Birch's construction to orthogonal modular forms and Clifford algebras, and applying a form of the Jacquet-Langlands correspondence. We also report on some limited computational evidence that this method can also be applied to GSp(4) Siegel modular forms. A short computer demonstration using Sage may be included if time permits. Note: this is a report on the PhD thesis of Jeffery Hein, written under John Voight at Dartmouth in consultation with Gonzalo Tornaria.

Some of the most fascinating pieces of mathematics,
such as Dirichlet's class number formula and the
celebrated Birch and Swinnerton-Dyer conjecture,
build a bridge between the distant worlds of arithmetic and analysis.
Euler systems and Iwasawa theory provide an intermediate step between the two, and both have been at the source of much of the progress to date on
BSD conjecture and its many generalizations. In this talk,
I will expand on some of these ideas, including a brief discussion of some of the recent developments in the area.

I will describe a class of modular compactifications of moduli spaces of elliptic surfaces. Time permitting, I will also discuss recent work towards connecting these compactifications with various existing compactifications of the moduli space of rational elliptic surfaces. This is joint work with Dori Bejleri.