# Spring 2023 Department Colloquium

Note that talks are listed in reverse chronological order.

### Tuesday 3/21 at 4:00-4:50

Speaker: Dr. Peter Vadasz (NAU Mechanical Engineering)

Title: Deterministic Quantum Mechanics

Abstract: A deterministic quantum mechanics theory is presented. The proposed theory is shown to be consistent with the current mainstream statistical quantum theory as well as with classical physics. It produces solutions, which demonstrate that causality, physical reality, and determinism are restored and can explain in simple form concerns that are raised by results from the current mainstream statistical quantum theory. The meaning of particle-wave duality and complementarity, the possibility of a particle, like the electron, to cross through the nucleus as it does when the angular momentum of the electron is zero at the ground state of the hydrogen atom, the possibility of a point-size particle to have an “intrinsic spin”, the possibility of “quantum jumps” as the electron transitions instantaneously from one stable orbital to another without passing through the space in between the orbitals and does that at irregular time intervals, and the natural collapse of the wave function as part of the solution are some of the results that emerge from the proposed deterministic quantum mechanics theory. The phenomenon of entanglement is also discussed in connection to the proposed theory and linked to the EPR paper and the Bell inequality violation by experiments demonstrating how non-locality and reality can coexist in realistic and classical form. Actual analytical solutions that are consistent with current mainstream quantum theory as well as with classical physics are presented via a linear stability method.

### Tuesday 2/28 at 4:00-4:50

Speaker: Dr. Steve Wilson (NAU-Emeritus)

Title: Transitive and Symmetric Cornerations in Maps

Abstract: When you’re looking for one thing, you find another. Sometimes it’s something even better. In trying to generalize “cycle structures”, we have found a simpler and maybe richer combinatorial object, based on “corners” in a map on a surface. In this talk, we will describe our motivating example, introduce corners and collections of corners (cornerations), prove a few results with entertaining proofs, and present interesting pictures throughout.

Note: The speaker will be giving a remote talk over Zoom (see email announcement for link). Many/most of us will be watching the presentation in Adel 164 as usual.

### Tuesday 2/21 at 4:00-4:50

Speaker: Dr. Brian Beaudrie and Dr. Angie Hodge-Zickerman (NAU)

Title: The Southwestern Section of the Mathematical Association of America: Past, Present, and Future

Abstract: In this interactive colloquium, you will learn about the MAA’s Southwestern Section. You will find out about its past, its present, and its future. When discussing the future of the Section, ample time will be allotted for the audience to voice what they would like to see from our MAA section. We encourage all to attend! We would like to hear from as many voices as possible in this session. Zoom option available.

### Tuesday 2/14 at 4:00-4:50

Speaker: Dr. Peter Vadasz (NAU Department of Mechanical Engineering)

Title: Deterministic Quantum Mechanics

Abstract: A deterministic quantum mechanics theory is presented. The proposed theory is shown to be consistent with the current mainstream statistical quantum theory as well as with classical physics. It produces solutions, which demonstrate that causality, physical reality, and determinism are restored and can explain in simple form concerns that are raised by results from the current mainstream statistical quantum theory. The meaning of particle-wave duality and complementarity, the possibility of a particle, like the electron, to cross through the nucleus as it does when the angular momentum of the electron is zero at the ground state of the hydrogen atom, the possibility of a point-size particle to have an “intrinsic spin”, the possibility of “quantum jumps” as the electron transitions instantaneously from one stable orbital to another without passing through the space in between the orbitals and does that at irregular time intervals, and the natural collapse of the wave function as part of the solution are some of the results that emerge from the proposed deterministic quantum mechanics theory. The phenomenon of entanglement is also discussed in connection to the proposed theory and linked to the EPR paper and the Bell inequality violation by experiments demonstrating how non-locality and reality can coexist in realistic and classical form. Actual analytical solutions that are consistent with current mainstream quantum theory as well as with classical physics are presented via a linear stability method.

### Thursday 1/19 at 4:00-4:50

Speaker: Dr. Robert Lund (University of California, Santa Cruz)

Title: Correlated Statistical Count Structures

Abstract: This talk overviews the statistical modeling of correlated count structures, including time series, spatial random fields, and space-time processes. In the time series setting, which constitutes the majority of this talk, some history and recent breakthroughs are presented. Classical approaches to the problem and their drawbacks are first reviewed. Next, a Gaussian copula is used to produce an extremely flexible count time series model that is naturally parsimonious, can have negative autocorrelations and/or long-memory features, can easily accommodate covariates, and can be statistically fitted by likelihood methods. An application to annual no-hitter counts in Major League baseball is given. The talk closes with extensions of the methods to the spatial and space-time settings.

### Thursday 1/24 at 4:00-4:50

Speaker: Michael Falk (NAU)

Title: A non-$K(\pi,1)$ factored line arrangement.

Abstract: In 1995 Luis Paris showed that arrangements of lines in the complex projective plane that are defined by equations with real coefficients and satisfy a certain factorization property have aspherical complements. More recently Gerhard Roehrle and his collaborators showed that the arrangement defined by the polynomial $Q(x,y,z)=x(x^3-y^3)(x^3-z^3)(y^3-z^3)(x+y+rz)$, where $r$ is a third root of 1, is factored. Recently I found a way to show this arrangement does not have aspherical complement, showing Paris’ theorem does not extend to arbitrary complex line arrangements. In this talk I’ll explain the context of the problem and sketch the entertaining proof, which amounts to elementary analytic geometry, albeit working in the complex plane, with an appearance of the main theorem of stratified Morse theory at the end. If there is time I’ll explain the connection with the pencils of curves that appear on Jim Swift’s web page. Joint work with Roehrle, aided by a long discussion during finals week with Michele Torielli and Quinn Beck.

### Thursday 1/19 at 4:00-4:50

Speaker: Alyssa Whittemore (former NAU undergraduate math major, recent PhD at University of Nebraska-Lincoln, currently senior research scientist at Boston Fusion)

Title: Bootstrap Percolation on Random Geometric Graphs

Abstract: Bootstrap percolation is a discrete-time process that models the spread of information or disease across the vertex set of a graph. We consider the following version of this process: Initially, each vertex of the graph is set active with probability $p$ or inactive otherwise. Then, at each time step, every inactive vertex with at least $k$ active neighbors becomes active. Active vertices will always remain active. The process ends when it reaches a stationary state. If all the vertices eventually become active, then we say we achieve percolation. This process has been widely studied on many families of graphs, deterministic and random. We analyze the bootstrap percolation process on a random geometric graph. A random geometric graph is obtained by choosing $n$ vertices uniformly at random from the unit $d$-dimensional cube or torus, and joining any two vertices by an edge if they are within a certain distance, $r$, of each other. We obtain very precise results that characterize the final state of the bootstrap percolation process in terms of the parameters $p$ and $r$ with high probability as the number $n$ of vertices tends to infinity.