Adiel Felsen, a junior dual majoring in computer science and mathematics, studies machine learning.

“Machines make mistakes but they make mistakes less often, especially if they’re trained properly,” Felsen says. “And there can be a lot of dangers in that if you start fully relying on only machines, but I really think machine learning is a great way forward for science in general.”

He has always had an interest in doing research, which played a part in his attraction to Binghamton and the Freshman Research Immersion program.

“I was interested before I went into the program, because the program is part of what attracted me to Binghamton,” Felsen says. “But it definitely allowed me to learn about topics that I wouldn’t otherwise learn until maybe senior year of school.”

FRI helped Felsen develop an understanding of data and machine learning. He categorizes data as anything from random images to letters and numbers. As a part of FRI, he worked on computer vision, a field of study where researchers teach computers how to complete simple tasks such as determining whether an image shows a cat or dog.

During his sophomore year, Felsen returned to FRI as a teacher assistant. In that role, Felsen not only assisted other students in understanding the basics of how to conduct research, he also solidified his own love for research.

Now working under Kenneth Chiu, associate professor of computer science; and Frank Lu, assistant professor of biomedical engineering, Felsen conducts research on biomedical imaging. He and his lab colleagues segment nuclei from cancer cells for SRS imaging.

SRS imaging, or stimulated Raman scattering microscopy, provides a detailed view of a cell. The method does not require the cell to be stained or dyed. Although it’s very fast, SRS imaging does not capture good contrast of DNA, and in biomedical imaging researchers need to be able to detect cell nuclei. Through machine learning algorithms, Felsen and his colleagues can improve the images’ contrast and see the nuclei.

One of Felsen’s mentors describes him as dynamic. “He has persistence and is always exploring new ideas,” Chiu says. “Those are the key things for research.”

Felsen will continue to develop his understanding of data and its many uses this summer as an intern at Mars Inc. He’ll work on projects dealing with data science for the chocolate company.

Felsen does not allow himself to be frustrated by minor setbacks because of what he sees as the impact of his work.

“Our research has the potential to help speed up the process of brain surgery, and it likely has a long way to go before it is actually implemented in the operating room,” Felsen says. “However, our research demonstrates that machine learning algorithms can improve the contrast of SRS images to look similar to stained cells. Hopefully, other researchers will see this promise and will be inspired to pursue similar work.”

When a high school math teacher saw a need for education reform, she ended up in the perfect position to make a difference.

Amber Simpson went back to school for her doctoral degree in curriculum and instruction in mathematics education at Clemson University. Now she’s an assistant professor of math education at Binghamton University.

“I had no idea what a PhD actually meant or required,” Simpson says. “But I started taking research classes and my world just flipped. I loved how you can contribute to the education field through research, and so that was a huge eye-opening experience for me, almost by happenstance.”

At Binghamton, Simpson says she has focused her research and coursework on changing the stigma associated with math education.

“Most students think of learning mathematics as, ‘Let me sit at my desk, listen to the teacher present procedures and do my homework,’” Simpson says. “But there’s a lot of research that supports the idea of inquiry, allowing kids to brainstorm ways to solve the problem through various approaches and having classroom discussions about their strategies.” 

In spring 2019, Simpson designed and taught a service-learning course called Making and Tinkering — an education class focused on design, physical creation and problem-solving. Students worked in groups to develop youth making programs. They implemented them in the community through a partnership with the Windsor Central School District and Your Home Public Library in Johnson City, Simpson says.

“Makerspaces provide a place for anyone to just go and make things, and tinker with things,” Simpson says. “Making can including high-tech tools such as 3D printers and laser cutters, low-tech tools such as makey-makeys and arduinos, or upcycled materials such as cardboard and yogurt containers. All of it has a huge presence within STEM education and as part of my research, I examine the role of making and tinkering for young children and educators.”

Jose A. Morales Collazo, a doctoral student in the department of teaching, learning and educational leadership, has worked with Simpson since she came to Binghamton in 2017. He attributes much of his success to her guidance.

“I was very intrigued by Dr. Simpson because she was this energetic person that was coming in with this fire,” Collazo says. “I waited a little bit, but then I just went to her office and knocked on her door and asked if I could help. … We started with just a smaller project that she was working on. And currently we are working on four projects involving STEM identity and meta-analysis.”

Simpson has published work in identity research, particularly STEM identity research, which is driven by her fascination of what people experience and their stories, she says. 

Aside from developing unique curricula, Simpson is involved in community research. She was awarded a three-year National Science Foundation grant to work with families and engineers on considering the engineering design process in their own home and/or community. Simpson says families are guided by local engineers and students on how to come up with solutions or prototypes for something they see as a problem.

“The family engagement piece is sort of a newer interest of mine,” Simpson says, “and I always try to build in identity research and making and tinkering into my projects. So this particular grant has all three of my research studies coinciding.”

Birthday conferences are a longstanding tradition in mathematics, but they’re not thrown for everybody, says Jim Davis, a mathematician from Indiana University. Farrell received this special honor, Davis says, because his work revolutionized the field of topology — an area of mathematics that explores the deformation of theoretical geometric objects.

Farrell is famous for formulating a theory with Stony Brook University mathematician Lowell Jones that came to be known as the Farrell-Jones Conjecture. The research began while Farrell studied at Yale in the 1960s. “My advisor suggested a couple of problems to work on, but then a few months later, he told me they’d been solved already by this person named Borel,” Farrell explains. “After this happened a few times, my advisor told me to go down to Princeton and ask Borel to suggest a problem for me to solve.” The problem he was assigned became known as the Borel Conjecture. “It’s what I’ve been working on for most of my life,” Farrell says.

The Borel Conjecture deals with geometric objects called manifolds, which often look like twisted ribbons or hollowed-out pretzels. Mathematicians who study manifolds have abstract ideas about shape. For example, you probably wouldn’t say that an egg and a sphere are the same shape, but in topology they’re thought of as homeomorphic: the points along their surfaces are arranged in a similar order. “There’s a saying that topologists don’t know the difference between a doughnut and a coffee mug,” Davis says. “The mug has a hole in the handle, so if it was made of clay, you could mold the mug into a doughnut.” But you can’t reshape an egg into a doughnut without tearing or gluing its surfaces, so those two objects are not homeomorphic.

What Armond Borel proposed was that if two manifolds have the same number of holes and a negatively curved surface (like the side of a nuclear power plant’s tower), then the manifolds would be homeomorphic — their points have a one-to-one correspondence. Some researchers disagreed with the conjecture. In 1988, after 21 years of puzzle-solving, Farrell and Jones were able to prove those dissenters wrong for most examples.

“Farrell, together with his advisor Wu-Chung Hsiang and later with Jones, did the most important work in proving this conjecture in many cases,” Davis says. “Farrell has said that in the beginning, some of the results were so surprising that even he didn’t believe it. It took a while for people to really understand it.”

Within the past few decades, the Farrell-Jones Conjecture has gained a following. The conjecture has been highlighted at the International Conference of Mathematicians, and a German mathematician named Wolfgang Leuck has founded an entire school of thought based on the Farrell-Jones Conjecture.

Davis says the Farrell-Jones Conjecture is a theoretical tool that has few real-world applications at this time.  But “when Einstein came along and needed mathematical tools for Theory of Relativity, he needed abstract differential geometry. The math developed 60 years earlier by (Bernhard) Riemann gave him a tool to use. So you never know! There’s a bunch of reasons why people like Tom and I can justify spending our lives doing mathematics. It can sometimes be influential, but the main thing is the sheer beauty in it.”

“Some mathematicians like to work on abstract things — they don’t care whether it is applicable or not,” Zacks says. “Usually what I like is to get a good applied problem and try to develop the mathematics around it. A model should not be built around some mathematical analysis just for the sake of doing mathematics alone.”

This interest in addressing real-world problems started right after he earned his bachelor’s degree in 1955 from Hebrew University of Jerusalem and began helping scientists at the Research Council of Israel understand their data using statistical methods.

“I loved those opportunities to work directly with scientists,” he says. “They were not working on routine problems and, hence, any conventional analysis was rarely appropriate.” So, to move the experiments forward, he had to be innovative, developing his own theories and methods.

Zacks kept his eye on the applicable during several appointments throughout the 1960s and ’70s. In 1976, because of his work on survival probabilities for particle crossing, a field having absorption points, a scientist at the White Sands Missile Range called to ask if he could apply his research to crossing minefields. Zacks said yes, and the collaboration lasted 10 years.

The research expanded as he worked with the Office of Naval Research and the U.S. Army Research Office to understand blind spots in other theaters as well. A big challenge facing submarines is icebergs obscuring much of the North Sea. Armies have a tough time fighting in forests because there are so many random variables that hide the target — the number of trees, tree width, enemy movement, ally movement, heaviness of foliage, etc. Put simply, Zacks helped the military figure out the probabilities of how much of the enemy could be seen and how much couldn’t.

While conducting that research, Zacks landed at Binghamton University in 1980, right when the mathematics academy was debating how mathematics could, or should, address the needs of private industry, which was clamoring for practical applications. Zacks revealed his position by establishing Binghamton University’s Center for Statistics to train IBM engineers in basic statistical quality control, reliability and design of experiments.

He worked with a colleague in the Thomas J. Watson School of Engineering and Applied Science to create simulations that ran on IBM’s first generation of PCs, which were used during seminars for the engineers. Later, other companies joined, including General Electric, Universal Instruments and Dupont, and Zacks partnered with them on several research projects.

At about the same time, he started working with a biostatistician at the Medical Center at Charleston, S.C., to develop cancer treatment experiments that would yield the best-quality data possible. Later, the design became more and more sophisticated as he worked with researchers at Philadelphia’s Fox Chase Cancer Center.

“We developed the methodology that tells them how to do the research — how many patients to take, how to randomize the patients, how long to do the trial,” Zacks says. “Basically, we are building the framework for the experiments. The question is, when they start getting results from the patients and see how they react, how do you incorporate these results into the theoretical framework so that it will tell them how to continue their research?”

Zacks, who was named a distinguished professor by the State University of New York last year, doesn’t maintain the editing load he used to (at one point he was the editor or on the editorial board of five scholarly journals simultaneously), but he’s still teaching and researching. Most recently, he has looked at distributions of stopping times, which has a wide range of applications, from telecommunications and computer servers to coffeehouse staffing and hospital wait times.

“They’re important objects in physics,” he said. “The more we can prove mathematically about these objects, the more data we have to use in research. Basically, there are models that govern different universes. Some of them come from Shimura varieties.”

Vasiu, associate professor of mathematics at Binghamton University, received his PhD from Princeton University. He joined the Binghamton faculty in 2007.

Vasiu received $156,933 in funding through the National Science Foundation for a project pertaining to solving important polynomial systems of equation over finite fields. “This is a central problem in number theory,” he said. “It is very much in the middle of several fields of mathematics, including algebra, analysis, combinatorics and geometry.”

Vasiu plans to write several papers and two books during the next two years, with help from two graduate students whose work will be supported by the American Recovery and Reinvestment Act-funded grant. He also has several collaborators in Germany and France.

“I hope these books will be used by generations of graduate students to come,” he said.