**Upcoming MAMS Colloquium Series**

### Spring 2024

**4/12/2024, Friday. 12:45-1:45 pm in Wickenden 321**

**Speaker**: Dr. Lixin Shen (Math Department, Syracus University)

**Title**: Computing Proximity Operators of Scale and Signed Permutation Invariant Functions

**Abstract**: This presentation focuses on computing proximity operators for scale and signed permutation invariant functions. A scale-invariant function remains unchanged under uniform scaling, while a signed permutation invariant function retains its structure despite permutations and sign changes applied to its input variables. Noteworthy examples include the $\ell_0$ function and the ratios of $\ell_1/\ell_2$ and its square, with their proximity operators being particularly crucial in sparse signal recovery. We delve into the properties of scale and signed permutation invariant functions, delineating the computation of their proximity operators into three sequential steps: the $\vw$-step, $r$-step, and $d$-step. These steps collectively form a procedure termed as WRD, with the $\vw$-step being of utmost importance and requiring careful treatment. Leveraging this procedure, we present a method for explicitly computing the proximity operator of $(\ell_1/\ell_2)^2$ and introduce an efficient algorithm for the proximity operator of $\ell_1/\ell_2$. This presentation is accessible to senior undergraduate and graduate students.

**4/5/2024, Friday. 12:45-1:45 pm in Clapp Hall 108**

**Speaker**: Dr. Persi Diaconis (Stanford University)

**Title**: The Mathematics of Solitaire

**Abstract**: Millions of people play solitaire (usual Klondike) every day. It is an embarrassment that mathematicians can’t answer the questions ‘what are the odds of winning?’, ‘What’s a good way of playing?’, In Vegas, you can ‘buy a deck’ for $52 and get $5 for each card played up. Is this fair? (HAH). I’ll report what we know; surely you say one of the fancy computer programs (alpha zero, mu zero) can do it (NOPE). There is a ‘simple solitaire’ where we can ‘do the math’. Surprisingly, this has links to some of the deepest corners of modern probability–random matrix theory–and the work of Elizabeth Meckes. I’ll try to explain all this in English, for a general audience.

**4/5/2024, Friday. 3:15-4:15 pm in Wickenden 321**

**Speaker**: Dr. Persi Diaconis (Stanford University)

**Title**: Adding numbers and shuffling cards

**Abstract**: When numbers are added in the usual way, ‘carries’ occur. For typical numbers, how do the carries go? How many are typical and, if you just had a carry, is it more or less likely that there will be a carry in the next column? It turns out that carries form a Markov chain with an ‘AMAZING’ transition matrix (are any matrices amazing?). This same matrix occurs in the analysis of the usual method of shuffling cards (riffle shuffling). I’ll explain the ‘seven shuffles theorem’ and the connection with carries. The same matrix occurs in taking sections of generating functions for the Veronese embedding and as the ‘Foulkes characters’ of the symmetric group. And then, well, carries are cocycles and the story goes on. I’ll try to explain it in ‘mathematical English’. This is joint work with Jason Fulman.

**3/29/2024, Friday. 3:15-4:15 pm in Wickenden 321**

**Speaker**: Dr. Michael Pokojovy (Old Dominion University)

**Title**: Univariate Fast Initial Response Statistical Process Control with Taut Strings

**Abstract**: We present a novel real-time univariate monitoring scheme for detecting a sustained departure of a process mean from some given standard assuming a constant variance. Our proposed stopping rule is based on the total variation of a nonparametric taut string estimator of the process mean and is designed to provide a desired average run length for an in-control situation. Compared to the more prominent CUSUM fast initial response (FIR) methodology and allowing for a restart following a false alarm, the proposed two-sided taut string (TS) scheme produces a significant reduction in average run length for a wide range of changes in the mean that occur at or immediately after process monitoring begins. A decision rule for when to choose our proposed TS chart compared to the CUSUM FIR chart that takes into account both false alarm rate and average run length to detect a shift in the mean is proposed and implemented. This is joint work with J. Marcus Jobe (Miami University, Oxford, OH).

**2/9/2024, Friday. 3:15-4:15 pm in Wickenden 321**

**Speaker**: Dr. Mona Merling (University of Pennsylvania)

**Title**: Higher scissors congruence invariants for manifolds

**Abstract**: The classical scissors congruence problem asks whether given two polyhedra with the same volume, one can cut one into a finite number of smaller polyhedra and reassemble these to form the other. There is an analogous definition of an SK (German “schneiden und kleben,” cut and paste) relation for manifolds and classically defined scissors congruence (SK) groups for manifolds. Recent work of Jonathan Campbell and Inna Zakharevich has focused on building machinery for studying scissors congruence problems via algebraic K-theory, and applying these tools to studying the Grothendieck ring of varieties. I will talk about a new application of this framework: we will construct a K-theory spectrum of manifolds, which lifts the classical SK group, and a derived version of the Euler characteristic. I will discuss what this higher homotopical lift of the Euler characteristic sees on the level of pi_1.