## Colloquium Schedule - Fall 2013 – Summer 2014 Abstracts

Wednesday, December 4th, 2013.  Mathematics Graduate Seminar.
Derrick Cox, UMaine Mathematics MA student
“The Metric Space Technique: the Means by which to Compare”
3:30 – 4:20 pm, Hill Auditorium, Barrows Hall (ESRB). (Snacks at 3:15 pm.)

The mathematical generalization of the notion of distance is a metric. A metric space is a set of elements together with a metric for measuring distance. Metrics generalize our ability to quantify similarities and differences between elements of a metric space. For example, the real plane together with the Euclidean distance is a metric space. Other metrics can be defined on the plane as well.

The Metric Space Technique is a mathematical formalism used to quantitatively compare the complex information in images. Instead of performing a pixel-by-pixel comparison between any two images, this method compares the images’ one dimensional “output functions”, which characterize specific morphological aspects in the images. From this, we can quantify similarities and differences between images. Hence, mathematical tools (like the Metric Space Technique) become an alternative to visual investigation and can provide quantitative and objective morphological analysis of images under study by calculating the metric distance between the imagesí output functions.

This talk should be accessible to undergraduates.

Wednesday, November 20th, 2013.  Mathematics Graduate Seminar.
Sophie Potozcak, UMaine Mathematics MA student
“Identification and Classification of Compact Surfaces”
3:30 – 4:20 pm, Hill Auditorium, Barrows Hall (ESRB). (Snacks at 3:15 pm.)

We will introduce the concept of compact surfaces. The sphere, the torus, and the Klein bottle are examples. We will discuss how to construct compact surfaces by gluing pairs of edges together in polygons and we will see that every compact surface can be represented in this way. Then we will prove a result that identifies all of the possible compact surfaces up to homeomorphism and we will introduce a result that distinguishes the possible compact surfaces using fundamental groups.

Thursday, November 14 and Thursday, November 21, 2013.  Mathematics Event.
Prof. Robert Franzosa, UMaine Mathematics
“Marston Morse, Morse Theory, and More”
3:30 – 4:20 pm, 100 Neville Hall.

A two meeting-event with:

• A viewing of Pits, Peaks, and Passes, a video that includes a 1965 lecture by Marston Morse on the basic ideas behind Morse Theory and includes an interview with Morse.
• A brief presentation by Bob Franzosa about Morse Theory and modern extensions.

Marston Morse is one of Maine’s most celebrated mathematicians. He was born in Waterville, Maine in 1892. He received his bachelor’s degree from Colby College in 1914, his master’s degree in 1915 from Harvard University, and his Ph.D. in 1917 from Harvard University. He taught at Harvard, Brown, and Cornell Universities before accepting a position in 1935 at the Institute for Advanced Study in Princeton where he remained until his retirement in 1962. His primary mathematical work was in global analysis and the calculus of variations. One of his accomplishments (that subsequently became known as Morse Theory) involved using local information about critical points of functions on a domain to infer global information about the structure of the domain.

In the 1960s through the 1980s Charles Conley at the University of Wisconsin developed generalizations of Morse Theory that subsequently became known as the Conley Index Theory. Bob Franzosa worked under Charles Conley for his Ph.D. and has, over the years, contributed to the development of the Conley Index theory. Current math department visitor Ewerton Vieria, a graduate student from Universidade Estadual de Campinas in Brazil, is working on aspects of the Conley Index Theory as part of  his Ph. D. research.

On Thursday November 14, 3:30-4:20, 100 Neville Hall, we will watch the 45-minute first part of Pits, Peaks, and Passes. (Popcorn will be served!!)

On Thursday November 21, 3:30-4:20, 100 Neville Hall, Bob Franzosa will give a brief presentation about Morse Theory and the Conley Index Theory. That will be followed by the 25 minute second part of Pits, Peaks, and Passes.

Wednesday, November 13, 2013.  Mathematics Colloquium.
Prof. John Thompson, UMaine Physics & Astronomy
“Investigating student understanding and application of mathematics needed in physics: Integration and the Fundamental Theorem of Calculus.”
3:30 – 4:20 pm, Hill Auditorium, 165 Barrows Hall (ESRB). (Snacks at 3:15 pm.)

Learning physics concepts often requires the ability to interpret and manipulate the underlying mathematical representations (e.g., equations, graphs, and diagrams). Moreover, physics students are expected to be able to apply mathematics concepts to find connections between various properties of a physical quantity (function), such as the rate of change (derivative) and the accumulation (definite integral). Results from our ongoing research into student understanding of thermal physics concepts have led us to investigate how students think about and use prerequisite, relevant mathematics, especially calculus, to solve physics problems.

We have developed or adapted questions related to the Fundamental Theorem of Calculus (FTC), specifically with graphical representations that are relevant in physics contexts, and often with parallel versions in both mathematics and physics. Written questions were administered initially; follow-up individual interviews were conducted to probe the depth of the written responses. Our findings are consistent with much of the relevant literature in mathematics education; we also have identified new difficulties and reasoning in students’ responses to the given FTC problems. In-depth analysis of the interview data suggests that students often fail to make meaningful connections between individual elements of the FTC while solving these problems.

Wednesday, November 6, 2013.  Pizza Pi Seminar.
Dr. Aitbala Sargent, UMaine Mathematics
“Mathematical models of ice sheet dynamics and their verification.”
3:30 – 4:20 pm, Hill Auditorium, 165 Barrows Hall (ESRB). (Pizza at 3:15 pm.)

How do ice sheets move?  What are the difficulties in modeling their dynamics?  Do the modelers have adequate mathematical models to describe their dynamics?  How are the models verified? This talk will give a short introduction to mathematical modeling of ice sheet dynamics and will try to answer the above questions.

Friday, November 1, 2013.  Mathematics Colloquium.
“Compressed sensing over the continuum”
3:30 – 4:30 pm, 100 Neville Hall.

Due to time, cost or other constraints, many problems one faces in science and engineering require the reconstruction of an object – an image or signal, for example – from a seemingly highly incomplete set of data.  Compressed sensing is a new field of research that seeks to exploit the inherent structure of real-life objects – specifically, their sparsity – to allow for recovery from such datasets.  Since its introduction a decade ago, compressed sensing has become an intense area of research in applied mathematics, engineering and computer science.  However, the majority of the theory and techniques of compressed sensing are based on finite-dimensional, digital models.  On the other hand, many, if not most, of the problems one encounters in applications are analog, or infinite-dimensional.

In this talk, I will present a theory and set of techniques for compressed sensing over the continuum.  I shall first motivate the need for this new approach by showing how existing finite-dimensional techniques fail for simple problems, due to mismatch between the data and the model.  Next I will argue that any theory in infinite dimensions requires new assumptions, which generalize the standard principles of compressed sensing (sparsity and random sampling with incoherent bases).  Using these, I will then develop the new theory and techniques.  Finally, I will show how this new approach allows for near-optimal recovery in a number of important settings.

Wednesday, October 23, 2013.  Mathematics Colloquium.
Prof. David Kung, St. Mary’s College of Maryland
“Harmonious Equations: A Mathematical Exploration of Music”
3:45 – 5:00 pm, Hill Auditorium, Barrows Hall (ESRB). (Snacks at 3:15 pm.)

Mathematics and music seem to come from different spheres (arts and sciences), yet they share an amazing array of commonalities. We will explore these connections by examining the musical experience from a mathematical perspective. The mathematical study of a single vibrating string unlocks a world of musical overtones and harmonics-and even explains why a clarinet plays so much lower than its similar-sized cousin the flute. Calculus, and the related field of differential equations, shows us how our ears hear differences between two instruments-what musicians call timbre-even when they play the same note at the same loudness. Finally, abstract algebra gives modern language to the structures beneath the surface of Bach’s magnificent canons and fugues. Throughout the talk, mathematical concepts will come to life with musical examples played by the speaker, an amateur violinist.

Wednesday, October 16, 2013.  Mathematics Colloquium.
Prof. Alain Arneodo, Ecole Normale Supérieure de Lyon
“Surfing on the genome: A tribute to Jean Morlet”
3:30 – 4:20 pm, 141 Bennett Hall. (Snacks at 3:15 pm.)

Recent technical progress in live cell imaging have confirmed that the structure and dynamics of chromatin play an essential role in regulating many biological processes, such as gene activity, DNA replication, recombination and DNA damage repair. The main objective of this talk is to show that there is a lot to learn about these processes when using multi-scale signal processing tools like the continuous wavelet transform (WT) to analyze DNA sequences.

In higher eukaryotes, the absence of specific sequence motifs marking the origins ofreplication has been a serious hindrance to the understanding of the mechanisms that regulate the initiation and the maintenance of the replication program in different cell types. During the course of evolution, mutations do not affect equally both strands of genomic DNA. In mammals, transcription-coupled nucleotide compositional skews have been detected but no compositional asymmetry has been associated with replication. In a first part, using a wavelet-based multi-scale analysis of human genome skew profiles, we identify a set of one thousand putative replication initiation zones. We report on recent DNA replication timing data that provide experimental verification of our in silico replication origin predictions. In a second part, we examine the organisation of the human genes around the replication origins. We show that replication origins, gene orientation and gene expression are not randomly distributed but on the opposite are at the heart of a strong organisation of human chromosomes. The analysis of open chromatin markers brings evidence of the existence of accessible open chromatin around the majority of the putative replication origins that replicate early in the S phase. We conclude by discussing the possibility that these “masterí replication origins also play a key role in genome dynamics during evolution and in pathological situations like cancer.

Dr. Arneodo is a physicist having worked at the interface between physics and biology/medicine for several decades. He is the leader and instigator of large interdisciplinary and international collaborative efforts. He obtained his thesis in Elementary Particle Physics at the University of Nice (France) in 1978. His scientific interest then shifted to dynamical system theory, leading him to the Centre de Recherche Paul Pascal in Bordeaux (France), to collaborate with the experimental group that was working at that time on chemical chaos. In 2002, he moved his research group to Ecole Normale Supérieure de Lyon (France) to build a new laboratory at the physics-biology interface. Dr. Arneodo’s scientific contribution encompasses many fields of modern physics including statistical mechanics, dynamical systems theory, chemical chaos, pattern formation in reaction-diffusion systems, fully-developed turbulence, the mathematics of fractals and multifractals, fractal growth phenomena, signal and image processing, wavelet transform analysis and its applications in physics, geophysics, astrophysics, chemistry, biology and finance. He is a Director of Research at the CNRS (Centre National de la Recherche Scientifique, France) and has published extensively in the physics literature, including over 275 peer-reviewed papers. He has trained 25 Doctors of Science. In 2005 he received the Prize of the Academie Royale des Sciences, Lettres et Beaux-Arts de Belgique, for his work in non-linear phenomena in physics and for his more recent interdisciplinary contributions to the bio / physics interface. Dr. Arneodo visits Maine every year in the Fall, where he teaches and interacts with students in the Graduate School of Biomedical Sciences and Engineering program, with faculty members of the Institute for Molecular Biophysics and with the CompuMAINE Laboratory.

Wednesday, October 9, 2013.  Mathematics Graduate Seminar.
Amber Hathaway, UMaine Mathematics MA student
“Emmy Noether’s Theorem in One Dimension”
3:30 – 4:20 pm, Hill Auditorium, Barrows Hall (ESRB). (Snacks at 3:15 pm.)

Noether’s Theorem provides a method for determining what quantities in a physical system are conserved. In this presentation we will derive the one-dimensional version of Emmy Noether’s Theorem in the case involving N dependent variables and first order derivatives.

Wednesday, October 2, 2013.  Mathematics Colloquium.
Dr. Sergey Lvin, UMaine Mathematics
“Differential identities for sin(x), $\mathbf{e^x}$, and x that came from medical imaging”
3:30 – 4:20 pm, Hill Auditorium, Barrows Hall (ESRB). (Snacks at 3:15 pm.)

We will introduce an infinite set of previously unknown differential identities for certain elementary functions, Including trigonometric and hyperbolic sines and cosines, exponential and linear functions.  These identities resemble the binomial formula and they initially appeared as a byproduct of our medical imaging research.  Some of the results are published in The American Mathematical Monthly in August-September 2013, some are new.

Students are welcome to attend.

Wednesday, September 25, 2013.  Pizza Pi Seminar.
Brian Toner, UMaine Mathematics MA student
“Math that Learns, the Mathematical Principles of Neural Networks and Machine Learning”
3:30 – 4:20 pm, Hill Auditorium, Barrows Hall (ESRB). (Snacks at 3:15 pm.)

A brief overview of Neural Networks, Machine Learning and the
mathematical machinery behind them.

Wednesday, September 18, 2013.  Mathematics Colloquium.
Prof. Robert Franzosa, UMaine Mathematics
“You Cannot Beat Bob In The Triangle Game Implies That A Beating Heart Cannot Respond In A Continuous Manner To A Stimulus Applied With Continuously Varying Strength And Timing”
3:30 – 4:20 pm, Hill Auditorium, Barrows Hall (ESRB). (Snacks at 3:15 pm.)

We will explore a game played on a triangular grid and see how properties of the game lead to the 2-dimensional Brouwer Fixed Point Theorem. Then we will see some interesting consequences of the Brouwer Fixed Point Theorem including the You-Are-Here Scenario and the No-Retraction Theorem. Finaly, one of the consequences will be applied to a simple heart-beat model to prove that a beating heart cannot respond in a continuous manner to an applied stimulus.