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Monday - Discovery Lecture Recap
“How microbes 'eat' and 'breathe' arsenic”
Professor Chad Saltikov
The first discovery lecture of the last week of COSMOS was an absolute thriller. Taught by Professor Chad Saltikov of the department of microbiology and Environmental Toxicology, it ran a deep breath into some of the smallest corners of our earth, specifically microbial life.
Saltikov first introduced his topic by explaining the effects of Arsenic for the everyday person. In the environment, two different types of arsenic are commonly found: Arsenite and Arsenate. The difference between the two being that the former binds sulfhydryl groups in many proteins, therefore potentially causing DNA damage. The latter on the other hand can mimic phosphate and can affect cellular energy production, and is much less toxic. While both different, all arsenic is extremely carcinogenic for all humans, and can cause multitudes of health issues such as cardiovascular disease and arsenicosis.
Humans are mainly exposed to arsenic through contaminated water or food. But not every person alive is at risk. Arsenic is geogenic in origin, meaning that in certain geographical locations, its supply may be higher than others. Whilst the list of problems that arsenic can cause for humans is extensive, there is little of a problem with arsenic consumption and contamination in developed countries due to regulations on water hygiene and supply. California, for example, has extremely high levels of arsenic in lakes, its soil, and water. Unfortunately, the same is untrue for developing countries like Bangladesh.
In Bangladesh, the arsenic problem has gotten out of hand, specifically in the meghna river region. Due to poor water regulations, and the prevalence of deep wells, arsenic has seeped into many drinking water supplies that are used by citizens everyday. The region has seen an unusual amount of arsenicosis, liver cancer, and cardiac arrest. Saltikov’s research primarily focused on finding a viable solution for the growing problem: what is a viable way to create a preventative measure for arsenic contamination? This is where microbes come into play.
Certain Microbes love to ‘eat’ arsenic. They have a specific name: Arsenotrophs. There are two primary types of Arsenotrophs as Saltikov explained, Oxidators and Reductors; crudely, ‘Eaters’ and ‘Breathers’ of arsenic, respectively. Oxidators are able to cycle arsenite into arsenate, the less harmful arsenic compound. Similarly, reductors are able to cycle arsenate into arsenite, the more toxic compound.
Potentially, to solve the rising arsenic contamination issue prevalentive throughout developing countries, Professor Saltikov found that using Oxidator Arsenotrophs could decrease the levels of more harmful arsenite and oxidise it into less harmful arsenate. While not solving the issue of arsenic contamination, it is one step forward into a growing field of research that COSMOS students were excitingly able to experience first hand at the last monday discovery lecture of UCSC 2026.
Written by Emily Halmer-Lee
Tuesday - Discovery Lecture Recap
“Coming to Terms: The Evolution of Modern Number Systems”
Professor Samuel Johnson
On Friday, Professor Johnson showed us the history and evolution of number systems, giving us many examples on how mathematicians have repeatedly expanded the idea of what a “number” is in order to solve new problems. He began with the natural numbers, which developed from humanity’s need to count, which then became an important foundation for science and mathematical discovery. Over time, mathematicians introduced integers and rational numbers, allowing them to represent negative quantities and fractions while still performing basic operations such as addition, subtraction, multiplication, and division.
However, mathematicians eventually discovered that rational numbers were not enough to describe every quantity. The ancient Greeks encountered this problem while studying the diagonal of a square, which has a length of 2 when each side has a length of one. Because 2 cannot be written as a fraction, it is an irrational number. The Greeks needed to find a way to represent this number that they could essentially hold in their hand (with a 1x1 square) but could not write/reason with. So, Professor Johnson showed us how the Babylonian method can approximate square roots by repeatedly making a guess, adjusting it, and averaging the results until the estimate becomes increasingly accurate. He also explained that numbers such as 2 are algebraic numbers because they are solutions/roots of polynomial equations with rational coefficients.
The lecture then shifted to a more modern perspective. He taught us that when an existing number system cannot solve a polynomial equation, mathematicians can construct a larger number system that includes the missing solutions. Professor Johnson introduced Galois groups, which study the symmetries among the roots of polynomial equations. For example, the roots of x4-2 can be represented as points arranged around a square, and the different ways those roots can be rearranged show important mathematical symmetries. He also explained that not every number is algebraic. Numbers such as and e are transcendental, meaning that they are not the roots of any polynomial equation with rational coefficients, even though they can still be approximated by rational numbers.
Professor Johnson then described how mathematicians “filled in the gaps” between rational numbers to construct the real numbers. Using ideas such as Cauchy sequences, mathematicians can study sequences of numbers that become closer and closer together, even when their limiting value is not rational. However, some equations still cannot be solved using real numbers. For example, x2+1 = 0 has no real solution, which led mathematicians to introduce the complex numbers and define i = -1. This expansion allows every polynomial equation to have a solution.
Toward the end of the lecture, Professor Johnson introduced local fields and p-adic numbers, which use a different way of measuring distance between numbers. Instead of relying only on the usual absolute value, p-adic systems measure how strongly numbers are related through their divisibility by a particular prime number, producing fractal-like geometric structures.
By the end of the lecture, Professor Johnson showed us that the modern number system was not created all at once. Instead, it was developed through centuries of mathematicians encountering new problems, discovering the limitations of existing numbers, and creating entirely new mathematical systems to overcome them.
Written by Clarina Manuel
Wednesday - Discovery Lecture Recap
“Neural Recordings Reimagined: Brain-Machine Interfaces at the Light Speed"
Professor Ali Yanik
Thursday - Discovery Lecture Recap
“Building Smarter, Safer Systems: Unlocking AI’s Potential for Autonomous Systems with Proven Performance and Robustness”
Professor Ricardo Sanfelice
In the last Discovery Lecture of COSMOS 2026, Professor Ricardo introduced us to the role of artificial intelligence in building smarter, safer, and more reliable autonomous systems. He first began by asking us, “What is AI?” Through an interactive Mentimeter activity, we learned how artificial intelligence can be defined as the ability of computers to perform tasks that normally require human intelligence. Professor Ricardo explained that AI uses math and logic to model intelligent behavior, and machine learning allows computers to identify patterns from data. He also told us about more advanced approaches, such as deep learning, which uses large neural networks to learn increasingly complex relationships. These technologies support applications ranging from computer vision and natural language processing to autonomous ground, air, and space vehicles.
Professor Ricardo then connected AI to autonomy and control theory. He used cruise control as an example of an autonomous system. In cruise control, the vehicle continuously monitors its speed and adjusts inputs using the throttle and brakes to maintain a desired output. This process forms a feedback loop, where a control algorithm repeatedly compares the system’s current behavior to its target and makes corrections. Unlike many AI systems, traditional control theory can provide mathematical guarantees about a system’s stability, performance, robustness, and safety.
Then, Professor Ricardo explained the limitations of AI-only systems. Although machine learning models can learn complex patterns and adapt to changing environments, they may struggle with unexpected situations that were not represented in their training data. Neural networks can also be difficult to interpret, making it challenging to prove that they will behave safely in every possible scenario. Failures involving autonomous vehicles and space systems show why strong safety guidelines are especially important when AI controls physical machines, but they are not always guaranteed.
To address these limitations, Professor Ricardo’s research combines the adaptability of AI with the mathematical reliability of control theory. For example, an autonomous drone may use machine learning to identify changing environmental conditions and adapt its behavior, while a traditional controller such as a PID controller acts as a reliable fallback when the learned system behaves unexpectedly. His lab also represents neural-network-based systems using state-space models, allowing researchers to analyze their behavior using reliable concepts from control theory.
Professor Ricardo described these combined systems as hybrid systems, which integrate discrete decision-making with continuous physical behavior. A thermostat is an example of a hybrid system- it uses continuous temperature measurements while making discrete decisions to turn heating or cooling systems on and off. His lab applies similar ideas to reinforcement learning through Hysteresis RL, which allows an AI system to switch between different learned policies while keeping track of which policy is currently active. This structured approach helps to safely apply AI to real-world tasks.
Finally, Professor Ricardo shared several applications for smarter and safer autonomy. Autonomous space vehicles could one day help repair, refuel, or assemble spacecraft and support large missions involving structures such as the International Space Station. AI-powered systems could also detect and predict the spread of fires or help robots identify and carefully pick ripe fruit, which is what his lab is working on! His main goal is to use AI to make systems more adaptable, and use control theory to make sure that they remain stable, robust, and safe.
As the final Discovery Lecture came to a close, Professor Ricardo showed us that the future of autonomous technology may depend not on choosing between AI and traditional control systems, but on combining the strengths of both. By integrating AI’s ability to learn with the reliable mathematical concepts of control theory, researchers can build autonomous systems that are not only smarter, but also safer and more trustworthy.
Written by Clarina Manuel
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