## Seminars and Colloquia by Series

### TBA by Po-Ling Loh

Series
School of Mathematics Colloquium
Time
Thursday, April 22, 2021 - 12:00 for 1 hour (actually 50 minutes)
Location
Zoom
Speaker
Po-Ling LohUniversity of Cambridge

Please Note: Note the unusual time: 12:00pm.

TBA

### TBA Victor Vilaça Da Rocha

Series
Analysis Seminar
Time
Wednesday, April 21, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Victor Vilaça Da RochaGeorgia Tech

### TBA by David Wood

Series
Graph Theory Seminar
Time
Tuesday, April 20, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
Speaker
David WoodMonash University

TBA

### Symmetrically processed splitting integrators for enhanced Hamiltonian Monte Carlo sampling

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 19, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE https://bluejeans.com/884917410
Speaker
Prof. Sergio BlanesUniversidad Politécnica de Valencia

We construct integrators to be used in Hamiltonian (or Hybrid) Monte Carlo sampling. The new integrators are easily implementable and, for a given computational budget, may deliver five times as many accepted proposals as standard leapfrog/Verlet without impairing in any way the quality of the samples. They are based on a suitable modification of the   processing technique first introduced by J.C. Butcher. The idea of modified processing may also be useful for other purposes, like the construction of high-order splitting integrators with positive coefficients.

Joint work with Mari Paz Calvo, Fernando Casas, and Jesús M. Sanz-Serna

### 3-manifolds that bound no definite 4-manifold

Series
Geometry Topology Seminar
Time
Monday, April 19, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Marco GollaUniversité de Nantes

All 3-manifolds bound 4-manifolds, and many construction of 3-manifolds automatically come with a 4-manifold bounding it. Often times these 4-manifolds have definite intersection form. Using Heegaard Floer correction terms and an analysis of short characteristic covectors in bimodular lattices, we give an obstruction for a 3-manifold to bound a definite 4-manifold, and produce some concrete examples. This is joint work with Kyle Larson.

### Approximate Schauder Frames for Banach Sequence Spaces

Series
Dissertation Defense
Time
Friday, April 16, 2021 - 16:00 for 1.5 hours (actually 80 minutes)
Location
ONLINE
Speaker
Yam-Sung ChengGeorgia Institute of Technology

The main topics of this thesis concern two types of approximate Schauder frames for the Banach sequence space $\ell_1$. The first main topic pertains to finite-unit norm tight frames (FUNTFs) for the finite-dimensional real sequence space $\ell_1^n$. We prove that for any $N \geq n$, FUNTFs of length $N$ exist for real $\ell_1^n$. To show the existence of FUNTFs, specific examples are constructed for various lengths. These constructions involve repetitions of frame elements. However, a different method of frame constructions allows us to prove the existence of FUNTFs for real $\ell_1^n$ of lengths $2n-1$ and $2n-2$ that do not have repeated elements.

The second main topic of this thesis pertains to normalized unconditional Schauder frames for the sequence space $\ell_1$. A Schauder frame provides a reconstruction formula for elements in the space, but need not be associated with a frame inequality. Our main theorem on this topic establishes a set of conditions under which an $\ell_1$-type of frame inequality is applicable towards unconditional Schauder frames. A primary motivation for choosing this set of hypotheses involves appropriate modifications of the Rademacher system, a version of which we prove to be an unconditional Schauder frame that does not satisfy an $\ell_1$-type of frame inequality.

### Mutation probabilities and moments of step functions

Series
Mathematical Biology Seminar
Time
Friday, April 16, 2021 - 15:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Zvi RosenFlorida Atlantic University

Suppose that n sample genomes are collected from the same population. The expected sample frequency spectrum (SFS) is the vector of probabilities that a mutation chosen at random will appear in exactly k out of the n individuals. This vector is known to be highly dependent on the population size history (demography); for this reason, geneticists have used it for demographic inference. What does the set of all possible vectors generated by demographies look like? What if we specify that the demography has to be piecewise-constant with a fixed number of pieces? We will draw on tools from convex and algebraic geometry to answer these and related questions.

### Symbolic dynamics and oscillatory motions in the 3 Body Problem

Series
CDSNS Colloquium
Time
Friday, April 16, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
Speaker
Pau MartinUPC

Consider the three body problem with masses $m_0,m_1,m_2>0$. Take units such that $m_0+m_1+m_2 = 1$. In 1922 Chazy classified the possible final motions of the three bodies, that is the behaviors the bodies may have when time tends to infinity. One of them are what is known as oscillatory motions, that is, solutions of the three body problem such that the positions of the bodies $q_0, q_1, q_2$ satisfy
$\liminf_{t\to\pm\infty}\sup_{i,j=0,1,2, i\neq j}\|q_i-q_j\|<+\infty \quad \text{ and }\quad \limsup_{t\to\pm\infty}\sup_{i,j=0,1,2, i\neq j}\|q_i-q_j\|=+\infty.$ At the time of Chazy, all types of final motions were known, except the oscillatory ones. We prove that, if all three masses $m_0,m_1,m_2>0$ are not equal to $1/3$, such motions exist. In fact, we prove more, since our result is based on the construction of a hyperbolic invariant set whose dynamics is conjugated to the Bernouilli shift of infinite symbols, we prove (if all masses are not all three equals to $1/3$) 1) the existence of chaotic motions and positive topological entropy for the three body problem, 2) the existence of periodic orbits of arbitrarily large period in the 3BP. Reversing time, Chazy's classification describes starting'' motions and then, the question if starting and final motions need to coincide or may be different arises.  We also prove that one can construct solutions of the three body problem whose starting and final motions are of different type.

### Two approximate versions of Jackson’s conjecture [Special time/day!]

Series
Combinatorics Seminar
Time
Thursday, April 15, 2021 - 18:00 for 1 hour (actually 50 minutes)
Location
Speaker
Anita LiebenauUNSW Sydney

A diregular bipartite tournament is a balanced complete bipartite graph whose edges are oriented so that every vertex has the same in- and outdegree.
In 1981, Jackson showed that a diregular bipartite tournament contains a Hamilton cycle, and conjectured that in fact the edge set of it can be partitioned into Hamilton cycles.
We prove an approximate version of this conjecture: for every $\epsilon>0$ there exists $n_0$ such that every diregular bipartite tournament on $2n>n_0$  vertices contains a collection of $(1/2-\epsilon)n$ cycles of length at least $(2-\epsilon)n$.
Increasing the degree by a small proportion allows us to prove the existence of many Hamilton cycles: for every $c>1/2$ and $\epsilon>0$ there exists $n_0$ such that every $cn$-regular bipartite digraph on $2n>n_0$ vertices contains $(1-\epsilon)cn$ edge-disjoint Hamilton cycles.

Base on joint work with Yanitsa Pehova, see https://arxiv.org/abs/1907.08479

Please note the special time/day: Thursday 6pm

### The parking model in Z^d

Series
Stochastics Seminar
Time
Thursday, April 15, 2021 - 15:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
David SivakoffThe Ohio State University

At each site of Z^d, initially there is a car with probability p or a vacant parking spot with probability (1-p), and the choice is independent for all sites. Cars perform independent simple, symmetric random walks, which do not interact directly with one another, and parking spots do not move. When a car enters a site that contains a vacant spot, then the car parks at the spot and the spot is filled – both the car and the spot are removed from the system, and other cars can move freely through the site. This model exhibits a phase transition at p=1/2: all cars park almost surely if and only if p\le 1/2, and all vacant spots are filled almost surely if and only if p \ge 1/2. We study the rates of decay of cars and vacant spots at, below and above p=1/2. In many cases these rates agree with earlier findings of Bramson—Lebowitz for two-type annihilating systems wherein both particle types perform random walks at equal speeds, though we identify significantly different behavior when p<1/2. Based on joint works with Damron, Gravner, Johnson, Junge and Lyu.

Online at https://bluejeans.com/129119189