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3/1 SIGMA Seminar -Minimal Subspaces and Where to Find Them: A Project in Reverse Math and Topology- Heidi Benham, Andrew DeLapo, Java Villano (UConn)
SIGMA Seminar -Minimal Subspaces and Where to Find Them: A Project in Reverse Math and Topology- Heidi Benham, Andrew DeLapo, Java Villano (UConn)
Friday, March 1st, 202412:20 PM - 01:10 PM Monteith BuildingThe Ginsburg-Sands theorem from topology states that every infinite topological space has an infinite subspace homeomorphic to exactly one of the following topologies on the natural numbers: indiscrete, discrete, initial segment, final segment, and cofinite. Ginsburg and Sands published their proof of this result in 1979 using consequences of the infinite version of Ramsey’s theorem for pairs. Ramsey’s theorem for pairs is also an important principle that shows up in reverse mathematics, so there are many natural questions a reverse mathematician might have about the proof of the Ginsburg-Sands theorem. Professors Damir Dzhafarov and Reed Solomon initiated an investigation into this theorem with Heidi, Andrew, and Java in Spring 2023. We worked in the context of countable second-countable (CSC) spaces, since CSC spaces are an ideal setting where topological principles can be studied using only second-order arithmetic, and we have many interesting results to share. We will each be highlighting the results from our paper, whose preprint was posted earlier this month. Java will discuss the strength of the general Ginsburg-Sands theorem as well as the complexity of finding the closure of a point – an important tool in the original proof by Ginsburg and Sands. Andrew will discuss the Ginsburg-Sands theorem restricted to Hausdorff spaces, and while this case is the most restrictive and is computably true, we found surprising results when restricting further to “effectively Hausdorff” spaces with “effectively discrete” subspaces. Heidi will discuss the Ginsburg-Sands theorem restricted to \(T_1\) spaces; as a principle in the Reverse Mathematics Zoo, we believe it is the first theorem from outside of logic to be strictly between Ramsey’s theorem for pairs and \(ACA_0\). We will start the presentation with the necessary background in computability and reverse math to ensure the talk is accessible to all math grad students.Contact Information: More
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3/2 Mathematics Continued Conference 2024
Mathematics Continued Conference 2024
Saturday, March 2nd, 202408:45 AM - 04:30 PM Monteith BuildingThe main goal of the conference is to give undergraduate students interested in math an idea of what graduate school may be like and to showcase some current research done by grad students and faculty members. The talks will be given at the level of a junior or senior-level undergraduate. We will also host a poster session for undergraduate students to display their research.
Contact Information:mcc@math.uconn.edu
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3/6 Francesco Bastianelli - Moving curves of least gonality on symmetric products of curves
Francesco Bastianelli - Moving curves of least gonality on symmetric products of curves
Wednesday, March 6th, 202411:15 AM - 12:05 PMGiven an irreducible projective variety \(X\), the covering gonality of \(X\) is the least gonality of an irreducible curve \(E\) contained in \(X\) and passing through a general point of \(X\).
In recent years, this birational invariant has been studied for various algebraic varieties, as e.g. hypersurfaces of the projective space and abelian varieties.
In this talk we will report on a joint work with Nicola Picoco, and we will be concerned with the covering gonality of the \(k\)-fold symmetric product \(C_k\) of a smooth complex projective curve \(C\) of genus \(g>k\).
In particular, we will show that for \(k=2,3,4\), the covering gonality of \(C_k\) equals the gonality of the curve \(C\).
Moreover, we will see that under mild assumptions of generality on \(C\), the only curves \(E\) passing through a general point of \(C_k\) and having the same gonality as \(C\) are copies of \(C\) of the form \(p+C\), where \(p\) is a point of \(C_\).Contact Information:Organizer Mihai Fulger mihai.fulger@uconn.edu
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3/6 Mathematical Finance and Applied Probability Seminar
Mathematical Finance and Applied Probability Seminar
Wednesday, March 6th, 202403:30 PM - 04:30 PM Monteith BuildingAbstract: We define and develop an approach for risk budgeting allocation – a risk diversification portfolio strategy – where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions that generalise the classical Euler contributions and which allow us to obtain dynamic risk contributions in a recursive manner. We prove that, for the class of coherent dynamic distortion risk measures, the risk allocation problem may be recast as a sequence of strictly convex optimisation problems. Moreover, we show that self-financing dynamic risk budgeting strategies with initial wealth of $1$ \new scaled versions of the solution of the sequence of convex optimisation problems. Furthermore, we develop an actor-critic approach, leveraging the elicitability of dynamic risk measures, to solve for risk budgeting strategies using deep learning.
Contact Information:Oleksii Mostovyi
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3/6 Math Club: The Gingerbread Man, by Dave McArdle (UConn)
Math Club: The Gingerbread Man, by Dave McArdle (UConn)
Wednesday, March 6th, 202405:30 PM Monteith 320The basic theory of difference equations will be introduced along with motivating examples that demonstrate the elegance and utility of the field. Specific attention will be given to several one-dimensional models with interesting dynamical properties. One of these models is the “gingerbread man” map. We will conclude with an overview of the type of research problems that are prominent in biological and epidemiological settings.Note: Free refreshments. The talk starts at 5:40.Contact Information: More
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3/8 SIGMA Seminar -Resilience through diversity: biophysical heterogeneity promotes stable activity in neuronal microcircuits- Scott Rich (UConn)
SIGMA Seminar -Resilience through diversity: biophysical heterogeneity promotes stable activity in neuronal microcircuits- Scott Rich (UConn)
Friday, March 8th, 202412:20 PM - 01:10 PM Monteith BuildingDiversity is the norm in most biological systems, and the brain is no exception: significant heterogeneity is observed in fundamental properties of similarly classified neurons in the human brain. Whether this variability drives physiological activity or is merely an epiphenomenon of noisy and stochastic biological processes remains an open question, although important initial evidence for a functional role for this diversity is found in the fact that it is reduced in neuropathology, particularly in the seizure-generating brain regions of patients with epilepsy. Applied mathematics is uniquely suited to mechanistically connect these heterogeneities to the dynamics of neuronal microcircuits using tools from the study of dynamical systems. In this seminar, I will review results from my postdoctoral research that strengthen the connection between heterogeneous neuronal circuits and resilience against pathological brain activity using bifurcation analysis, and preview how my interdisciplinary laboratory at the University of Connecticut will further delineate how experimentally-relevant heterogeneities drive physiological brain activity of functional relevance.
Contact Information: More
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3/8 Annual Logic Lecture: Denis Hirschfeldt
Annual Logic Lecture: Denis Hirschfeldt
Friday, March 8th, 202402:00 PM MCHU 201 & ZoomAbstract
Many mathematical principles can be stated in the form “for all X such that C(X) holds, there is a Y such that D(X,Y) holds”, where X and Y range over second-order objects, and C and D are arithmetic conditions. We can think of such a principle as a problem, where an instance of the problem is an X such that C(X) holds, and a solution to this instance is a Y such that D(X,Y) holds. I will discuss notions of reducibility between such problems coming from the closely-related perspectives of reverse mathematics and computability theory.Contact Information:logic@uconn.edu
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3/20 Türkü Özlüm Çelik - Riemann Theta Functions Today
Türkü Özlüm Çelik - Riemann Theta Functions Today
Wednesday, March 20th, 202411:00 AM - 12:05 PMTheta functions play a central role in various branches of mathematics. In this talk, we will showcase their significance in algebra and geometry, particularly in studying complex algebraic curves with applications in soliton equations. We will explore how these applications can address the Schottky problem, a classical geometry problem, thereby spotting a mutually enriching relationship. An emphasis will be on exploiting current trends in nonlinear algebra to advance our understanding of this interconnection, encompassing both symbolic and numerical computational approaches.
Contact Information:organizer Mihai Fulger (mihai.fulger@uconn.edu)
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3/20 Math Club: Partitions and \(q\)-binomial coefficients, by Blake Jackson (UConn)
Math Club: Partitions and \(q\)-binomial coefficients, by Blake Jackson (UConn)
Wednesday, March 20th, 202405:30 PM Monteith 320A partition of an integer \(n \geq 1\) is a way of writing \(n\) as a sum of positive integers: 4 has the five partitions 4, 2+2, 1+3, 1+1+2, and 1+1+1+1, while 100 has around 190,000,000 partitions! There is no known formula for the number of partitions of \(n\) in general, but that hasn’t stopped mathematicians from finding interesting properties of partitions for over 300 years.
In this talk, which is a preview of next semester’s course on algebraic combinatorics (Math 3094) we will play a game of Bulgarian Solitaire, explore integer partitions, and meet \(q\)-binomial coefficients, which are polynomials that both resemble binomial coefficients and are related to integer partitions. At the end of the talk, we will use the knowledge that we gained to compute \((A+B)^n\) when \(AB \not= BA\) (e.g., matrices).
Note: Free refreshments. The talk starts at 5:40.
Contact Information: More
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3/22 SIGMA Seminar - Quantum Mechanics as a Deformation of Classical Mechanics- Dion Mann (UConn)
SIGMA Seminar - Quantum Mechanics as a Deformation of Classical Mechanics- Dion Mann (UConn)
Friday, March 22nd, 202412:20 PM - 01:10 PM Monteith BuildingWith nearly every discovery, it is often the case that physical theory must be modified to remain consistent with modern observations. One should expect a new physical theory to approximately recover the predictions of the previous in some limiting behavior. Thus we can view the emergence of new physics as a sort of “deformation” of old physics. As a prototypical example, the ancient flat Earth deforms through modern manifold theory into a sphere, and modern manifold theory recovers observations made in a flat world by zooming in very closely. Under this motivation, we interpret quantum mechanics as a deformation of classical mechanics via a mathematically rigorous program called “deformation quantization.” Here, quantum mechanics is a deformed classical theory, whose deformation is measured by Planck’s constant \(\hbar\), and whose limiting behavior \(\hbar \to 0\) will represent a contraction back to classical theory. The purpose of this talk is to give a friendly introduction to the program and review some recent progress.
Contact Information: More
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3/22 Logic Colloquium: James Walsh (NYU)
Logic Colloquium: James Walsh (NYU)
Friday, March 22nd, 202402:00 PM MCHU 201 & ZoomJoin us for a talk by James Walsh (NYU)!
“Is the consistency operator canonical?”
https://logic.uconn.edu/calendar/Contact Information:logic@uconn.edu
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3/25 PDE and Differential Geometry Seminar, Variational Analysis of some nonlocal energy functionals and associated function spaces, Tadele Mengesha (University of Tennessee)
PDE and Differential Geometry Seminar, Variational Analysis of some nonlocal energy functionals and associated function spaces, Tadele Mengesha (University of Tennessee)
Monday, March 25th, 202402:30 PM - 03:30 PM Monteith BuildingAbstract: I will present a recent work on variational problems involving nonlocal energy functionals that appear in nonlocal mechanics. I will discuss the associated function spaces, which are nonstandard, and establish some properties that will make it possible to pose a uniquely solvable nonlocal variational. I will discuss some difficulties in proving fundamental structural properties of the function spaces such as compactness. For a sequence of parametrized nonlocal functionals in suitable form, we compute their variational limit and establish a rigorous connection with classical models.
Contact Information:xiaodong.yan@uconn.edu
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3/27 Algebra Seminar - Results in Prym-Brill-Noether theory by Andrei Bud
Algebra Seminar - Results in Prym-Brill-Noether theory by Andrei Bud
Wednesday, March 27th, 202411:00 AM - 12:05 PMMany results about the geometry of the moduli space of curves \(\mathcal_g\) are obtained via Brill-Noether Theory. When studying Prym curves \([C,\eta]\) (i.e., curves together with a \(2\)-torsion line bundle) we can consider Brill-Noether loci taking the extra structure into account.
We will study Prym-Brill-Noether loci at the level of moduli, and prove the irreducibility of the universal Prym-Brill-Noether locus.
Contact Information:organizer Mihai Fulger mihai.fulger@uconn.edu
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3/27 Math Club: Continuous nowhere differentiable functions, by Michael Albert (UConn)
Math Club: Continuous nowhere differentiable functions, by Michael Albert (UConn)
Wednesday, March 27th, 202405:30 PM Monteith 320Some continuous functions are not differentiable at one number, like \(|x|\)
at \(x = 0\). Using a graph with corners at \(0, \pm 1, \pm 2, \ldots\), we can build
continuous functions that are not differentiable at infinitely many numbers that are separated from each other.It was commonly believed that a continuous function could be non-differentiable only at a “small” set of numbers until the 1870s, when Weierstrass found a continuous function that is not differentiable anywhere! These wild functions have applications today in mathematical finance, where continuous nowhere differentiable sample paths of Brownian motion are used to model stock prices.
In this talk we will see how to construct a continuous function that is differentiable nowhere. It will be accessible to anyone who has taken Calculus I and II.Note: Free refreshments. The talk starts at 5:40.
Contact Information: More
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3/29 SIGMA Seminar - An Exposé of Overly Complicated Ways to Prove Easy Facts- Ben Oltsik (UConn)
SIGMA Seminar - An Exposé of Overly Complicated Ways to Prove Easy Facts- Ben Oltsik (UConn)
Friday, March 29th, 202412:20 PM - 01:10 PM Monteith BuildingHave you ever seen a mosquito and wanted to shoo it away? Certainly, if you used a nuclear bomb, this would solve the issue, despite there being many simpler ways to approach the problem. Today, we discuss the mathematical equivalent of this. In particular, we explore some ways to prove fairly elementary facts using overly advanced results.
Contact Information: More
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3/29 Logic Colloquium: Ainsley May (UC Irvine)
Logic Colloquium: Ainsley May (UC Irvine)
Friday, March 29th, 202402:00 PM ZoomJoin us for a talk by
Ainsley May (UC Irvine):
“Meaning in Mathematics: a folkloric account”
Current accounts of meaning in mathematics face a dilemma between triviality and over-specificity. On the one hand, intensional accounts of meaning such as possible world semantics give the trivial result that every mathematical theorem has the same meaning since they are all necessarily true. This triviality is unsatisfactory because we clearly hold some mathematical theorems have different meanings from others. On the other hand, hyperintensional accounts like impossible worlds and structured propositions allow us to distinguish between necessary truths. However, they are so fine-grained that it becomes difficult to uniformly identify the salient semantic features.
In response to this dilemma, I propose an account of mathematical meaning called the folkloric account. On the folkloric account the content of a mathematical theorem is the collection of models, within some reference class of models, that make the theorem true. The appeal of this account is partly that it retains central aspects of world-based accounts, such as evaluation within a model. Yet it overcomes their limitations by incorporating more models to represent different mathematical theories and structures without allowing absolutely every such structure. Here, I introduce the folkloric account and use examples to highlight some of its strengths and identify weaknesses to address in future research.Contact Information:logic@uconn.edu
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