Mathematics Commons^™

Nonstandard Dice That Both Count For Card Craps, Mark Bollman

International Conference on Gambling & Risk Taking

The Pala Casino in California deals Card Craps using a red die numbered {2; 2; 2; 5; 5; 5} and a blue die numbered {3; 3; 3; 4; 4; 4}. Two cards from a special 36-card deck, which contains one card bearing each of the 36 ways in which two dice can land when rolled, are dealt: one each face down to a red space and a blue space. When the dice are rolled, the higher number determines which of the cards is flipped over.

A moment's reflection reveals that Pala's blue die is unnecessary. The card selection process can …

A 3d Numerical Study Of Interface Effects Influencing Viscous Gravity Currents In A Parabolic Fissure, With Implications For Modeling With 1d Nonlinear Diffusion Equations, Eden Furtak-Cole, Aleksey S. Telyakovskiy

Mathematics and Statistics Student Research and Class Projects

Although one-dimensional non-linear diffusion equations are commonly used to model flow dynamics in aquifers and fissures, they disregard multiple effects of real-life flows. Similarity analysis may allow further analytical reduction of these equations, but it is often difficult to provide applicable initial and boundary conditions in practice, or know the magnitude of effects neglected by the 1D model. Furthermore, when multiple simplifying assumptions are made, the sources of discrepancy between modeled and observed data are difficult to identify. We derive one such model of viscous flow in a parabolic fissure from first principals. The parabolic fissure is formed by extruding …

Lecture 10, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Continuation of Fyodorov--Keating conjectures, connections with random multiplicative functions.

Lecture 9, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Fyodorov--Keating conjectures, connections with random multiplicative functions.

Exploration Using Without-Replacement Sampling Of Actions Is Sometimes Inferior, Stephen W. Carden, S. Dalton Walker

Mathematical Sciences: Faculty Publications

In many statistical and machine learning applications, without-replacement sampling is considered superior to with-replacement sampling. In some cases, this has been proven, and in others the heuristic is so intuitively attractive that it is taken for granted. In reinforcement learning, many count-based exploration strategies are justified by reliance on the aforementioned heuristic. This paper will detail the non-intuitive discovery that when measuring the goodness of an exploration strategy by the stochastic shortest path to a goal state, there is a class of processes for which an action selection strategy based on without-replacement sampling of actions can be worse than with-replacement …

The Weyl Bound For Dirichlet L-Functions, Matthew P. Young

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Abstract: In the 1960's, Burgess proved a subconvexity bound for Dirichlet L-functions. However, the quality of this bound was not as strong, in terms of the conductor, as the classical Weyl bound for the Riemann zeta function. In a major breakthrough, Conrey and Iwaniec established the Weyl bound for quadratic Dirichlet L-functions. I will discuss recent work with Ian Petrow that generalizes the Conrey-Iwaniec bound for more general characters, in particular arbitrary characters of prime modulus.

Extension Of A Positivity Trick And Estimates Involving L-Functions At The Edge Of The Critical Strip, Xiannan Li

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Updated schedule

Abstract: I will review an old trick, and relate this to some modern results involving estimates for L-functions at the edge of the critical strip. These will include a good bound for automorphic L-functions and Rankin-Selberg L-functions as well as estimates for primes which split completely in a number field.

Lecture 8, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Continuation of Extreme values of L-functions.

Lecture 7, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Extreme values of L-functions.

Weighted Composition Operators On The Hilbert Hardy Space Of A Half-Plane, Valentin Matache

Mathematics Faculty Publications

Operators of type f→ψf∘ϕ acting on function spaces are called weighted composition operators. If the weight function ψ is the constant function 1, then they are called composition operators. We consider weighted composition operators acting on the Hilbert Hardy space of a half-plane and study compactness, boundedness, invertibility, normality and spectral properties of such operators.

Lecture 6, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Continuation of Progress towards moment conjectures -- upper and lower bounds.

Lecture 5, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Progress towards moment conjectures -- upper and lower bounds.

Forward Selection Via Distance Correlation, Ty Adams

Mathematical Sciences Technical Reports (MSTR)

No abstract provided.

Domain Restrictions In Strategy-Proof Social Choice., Gopakumar Achuthankutty Dr.

Doctoral Theses

In Chapter 2, we consider domains of admissible preferences with a natural property called top-circularity. Several domains with practical applications such as multidimensional single-peaked domain in [9], union of a single-peaked and a single dipped domain, etc. satisfy top-circularity. We show that if such a domain satisfies either the maximal conflict property or the weak conflict property, then it is dictatorial. We show that this result can be applied to the problem of locating a public facility where the planner does not know whether agents derive positive or negative externality from the facility. The union of a single-peaked and a …

High Moments Of L-Functions, Vorrapan Chandee

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Abstract: Moments of L-functions on the critical line (Re(s) = 1/2) have been extensively studied due to numerous applications, for example, bounds for L-functions, information on zeros of L-functions, and connections to the generalized Riemann hypothesis. However, the current understanding of higher moments is very limited. In this talk, I will give an overview how we can achieve asymptotic and bounds for higher moments by enlarging the size of various families of L-functions and show some techniques that are involved.

Moments Of Cubic L-Functions Over Function Fields, Alexandra Florea

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Abstract: I will talk about some recent work with Chantal David and Matilde Lalin about the mean value of L-functions associated to cubic characters over F_q[t] when q=1 (mod 3). I will explain how to obtain an asymptotic formula which relies on obtaining cancellation in averages of cubic Gauss sums over functions fields. I will also talk about the corresponding non-Kummer case when q=2 (mod 3) and I will explain why this setting is somewhat easier to handle than the Kummer case, which allows us to prove some better results.

Lecture 4, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Larger values of L-functions on critical line -- moments, conjectures.

Lecture 3, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Continuation of Selberg's central limit theorem and analogues in families of L-functions (typical size of values on critical line).

An Effective Chebotarev Density Theorem For Families Of Fields, With An Application To Class Groups, Caroline Turnage-Butterbaugh

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

This talk will present an effective Chebotarev theorem that holds for all but a possible zero-density subfamily of certain families of number fields of fixed degree. For certain families, this work is unconditional, and in other cases it is conditional on the strong Artin conjecture and certain conjectures on counting number fields. As an application, we obtain nontrivial average upper bounds on ℓ-torsion in the class groups of the families of fields.

Landau-Siegel Zeros And Their Illusory Consequences, Kyle Pratt

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Updated time

Abstract: Researchers have tried for many years to eliminate the possibility of LandauSiegel zeros—certain exceptional counterexamples to the Generalized Riemann Hypothesis. Often one thinks of these zeros as being a severe nuisance, but there are many situations in which their existence allows one to prove spectacular, though illusory, results. I will review some of this history and some of these results. In the latter portion of the talk I will discuss recent work, joint with H. M. Bui and Alexandru Zaharescu, in which we show that the existence of Landau-Siegel zeros has implications for the behavior of Dirichlet …