Special Lecture Archives for Fall 2024 to Spring 2025
A Gentle Introduction to Quantum Computing for Mathematicians (Part 1) - MathQuantum RTG Lecture
When: Thu, September 28, 2023 - 2:00pmWhere: PSC 1136
Speaker: Konstantina Trivisa (Mathematics and IPST) - https://www.math.umd.edu/~trivisa/
Abstract: The lecture will present elements from early history and make references to some of the giants in quantum computation, starting with Richard Feynman and Yuri Manin. It will then give a picture of the State of the Art today as far as available hardware is concerned after introducing some basic concepts: qubit, measurement, superposition and entanglement.
During his lifetime, Feynman (an American theoretical physicist) became one of the best known scientists in the world. Yuri Manin (a Russian mathematician) was known for work in algebraic geometry and diophantine geometry. Both of them independently advocated the idea of "computation grounded in physics", which led to the modern concept of quantum computation and the idea of storing and processing information.
The involvement of Mathematicians has been crucial since the beginning of quantum information science. It was another mathematician Peter Shor who in 1994 discovered a polynomial-time algorithm for factoring numbers igniting a flurry of activity that created the field of quantum information.
Coffee and snacks will be provided
RSVP appreciated at: https://forms.gle/jYUa1v1NPN5VPyQs5
Taming the Quantum World (MathQuantum Movie Night)
When: Thu, October 12, 2023 - 5:00pmWhere: Iribe Antonov Auditorium (0324)
Speaker: MathQuantum RTG (IPST) - https://mathquantum.umd.edu
Abstract: Join us for a movie, pizza and discussion, while meeting others at UMD interested in quantum computing! Anyone curious about quantum technology and its applications is welcome, regardless of expertise.
RSVP appreciated: https://forms.gle/jYUa1v1NPN5VPyQs5
Taming the Quantum World (46min) is a 2013 documentary by Lars Becker-Larsen about the development of quantum computers. At this movie night, we will watch the film, and follow it by small- and large-group critical discussion. We will delve into topics such as
- What can audiences of different backgrounds get out of a film like this?
- How is quantum computing represented in popular media (paying attention to accuracy and hype)?
- How have our knowledge and perceptions about quantum computers changed in the 10 years since this film was made?
This event is co-organized by the IPST MathQuantum RTG and the Undergraduate Quantum Association
Workshop: Connecting My Interests with Quantum Information Science
When: Thu, October 19, 2023 - 2:00pmWhere: PSC 1136
Speaker: Franz Klein, Carl Miller, Daniel Serrano (IPST) - https://mathquantum.umd.edu
Abstract: RSVP required at https://forms.gle/jYUa1v1NPN5VPyQs5. Coffee and snacks will be provided.
Come explore how you could fit in the world of Quantum Information Science (QIS) research. In this workshop, we will guide you to map the connections between your existing interests/skills and QIS.
The event will consist of a short intro lecture, guided exercises, feedback on your ideas, informal presentations by participants, and group discussion. By the end of the workshop, you will have a draft QIS research question.
This event is primarily intended for two audiences: (i) Math grad students and postdocs who are curious to know more about QIS (ii) grad students and postdocs (any field) already working in QIS, who want to integrate more advanced Math into their work
Undergrad students in the two categories above are also welcome if they have good familiarity with doing literature searches.
Students/postdocs outside of Math/QIS are also welcome, but please let Daniel know ahead of time your intent to participate and your discipline.
Additional logistics:
- Please bring a laptop to engage in all activities.
- The workshop will be 2h long.
- This workshop is limited capacity in order to allow for meaningful engagement. RSVP is required so we have a clear headcount.
- Participants familiar with doing literature searches (using Web of Science, Google Scholar, ResearchRabbit, etc.) will be able to make the most out of this workshop. Participants without this familiarity are welcome, but we appreciate if you let Daniel know ahead of time that you might need assistance with this.
The Perils of Averaging Averages
When: Mon, October 23, 2023 - 3:15pmWhere: Kirwan Hall 3206
Speaker: Chris Laskowski (UMD) - https://www.math.umd.edu/~laskow/
Abstract: The Distinguished Scholar-Teacher Program, established in 1978, honors a small number of faculty members each year who have demonstrated notable success in both scholarship and teaching. By honoring the Distinguished Scholar-Teachers with this prestigious award, we reaffirm our commitment to excellence in teaching and scholarship. The Distinguished Scholar-Teacher Program is sponsored by the Office of Academic Affairs and administered by the Associate Provost for Faculty Affairs.
Research Success Stories at the Intersection of Mathematics and Quantum Information Science
When: Thu, November 9, 2023 - 2:00pmWhere: PSC 1136
Speaker: Gorjan Alagic, Dong An, Carl Miller (QuICS) - https://mathquantum.umd.edu
Abstract:
RSVP at https://forms.gle/jYUa1v1NPN5VPyQs5. Snacks and coffee will be provided.
In this session, three researchers will share how they entered the field of Quantum Information Science coming from a Mathematics background, followed by an overview of their current work at the intersection of these two disciplines.
Gorjan Alagic is an Associate Research Scientist at QuICS and UMIACS. His research lies at the intersection of theoretical computer science and mathematics, with a particular focus on quantum algorithms and cryptography.
He previously held research positions at Caltech, the University of Waterloo, and the University of Copenhagen. He did his doctorate work with Alexander Russell at the University of Connecticut.
Dong An is a QuICS Hartree Postdoctoral Fellow in quantum information science. His research interests include quantum algorithms, computational quantum mechanics, and an interdisciplinary study on quantum computing and applied mathematics.
He received his doctorate in Applied Mathematics from University of California, Berkeley in 2021.
Carl Miller is an Adjunct Associate Professor at QuICS and a Mathematician in the Computer Security Division at NIST. He studies new cryptography for the quantum era, including topics such as verifiable random number generation, quantum protocols between mutually mistrustful parties, and classical "postquantum" cryptography.
Miller received a Ph. D. in Mathematics from Berkeley in 2007, followed by a research fellowship in the Electrical Engineering and Computer Science Department at the University of Michigan.
(Bios adapted from https://quics.umd.edu)
A Gentle Introduction to Quantum Computing for Mathematicians Part 2
When: Tue, November 28, 2023 - 3:00pmWhere: PSC 1136
Speaker: Konstantina Trivisa (Math and IPST) - https://www.math.umd.edu/~trivisa/
Abstract: Join us for Part 2 of this lecture, which will continue introducing quantum computing from a mathematical point of view.
Part 1 covered historical perspectives of math and computing that led to the current status of quantum computing. It then introduced some basic concepts like qubit, measurement, superposition and entanglement. To recap, you can access a recording at https://youtu.be/FMfjwVIBaws
RSVP at https://forms.gle/jYUa1v1NPN5VPyQs5.
Coffee and snacks will be provided.
Properties of Spin Glasses and their Mixing Times
When: Tue, November 28, 2023 - 3:30pmWhere: Kirwan Hall 3206
Speaker: Arka Adhikari (Stanford University) - https://arkaa.people.stanford.edu/
Abstract: Statistical physics is a branch of physics that uses probability theory in order to model physical systems with large numbers of particles. Foundational concepts and models from this subject have been used in a wide variety of fields, including AI and big data. In this talk, I will explore the properties of spin glasses, a model of disordered magnetic systems. I will go over many fundamental aspects
of the physical behavior of spin glasses and the mixing and speed of some dynamics on spin glasses.
Quantum Information Science for Quantum Gravity (MathQuantum Seminar)
When: Thu, November 30, 2023 - 2:00pmWhere: PSC 2136
Speaker: Anil Zenginoglu (IPST) - https://anilzen.github.io
Abstract: Coffee and snacks will be provided
RSVP appreciated but not needed: https://forms.gle/jYUa1v1NPN5VPyQs5
While Quantum Mechanics and General Relativity have been experimentally tested extensively, they stand as incompatible theories, challenging our fundamental understanding of the Universe. The quest to construct a consistent theory of Quantum Gravity stands at the frontier of research in theoretical physics. In the last few decades, concepts from Quantum Information Science, such as entanglement and complexity, have started playing a central role in this quest.
This seminar will provide an overview of the intersection between Quantum Information Science and Quantum Gravity at a popular science level. We will discuss black holes, entropy, information, the holographic principle, AdS/CFT correspondence, quantum entanglement, and quantum complexity, scraping the surface of deep connections between information and gravity.
Invasion in several guises
When: Mon, December 4, 2023 - 4:00pmWhere: Kirwan Hall 3206
Speaker: Cole Graham (Brown University) -
Abstract: The world teems with examples of invasion, in which one steady state spatially invades another. Invasion can even display a universal character: fine details recur in seemingly unrelated systems. Reaction-diffusion equations provide a mathematical framework for these phenomena. In this talk, I will discuss recent examples of robust invasion patterns in reaction-diffusion equations, with an emphasis on multiple dimensions.
Onsager conjecture: A glimpse of turbulence
When: Tue, December 5, 2023 - 1:45pmWhere: Kirwan Hall 3206
Speaker: Hyunju Kwon (ETH) -
Abstract: Abstract: In the study of fluid dynamics, turbulence poses a significant challenge in predicting fluid behavior, and it remains a mystery for mathematicians and physicists alike. Recently, there has been some exciting progress in our understanding of ideal turbulence: starting from Onsager’s theorem to the resolution of strong Onsager's conjecture in $L^3$-framework. These developments have been accompanied by mathematical advances in Nash’s iteration. In this talk, I will provide an overview of turbulence and discuss these results.
Recent developments in p-adic geometry and the local Langlands correspondence
When: Wed, December 6, 2023 - 2:00pmWhere: Kirwan Hall 3206
Speaker: Ian Gleason (University of Bonn)
Abstract:
The local Langlands correspondence, proposed by Langlands as the non-abelian analogue of local class field theory for non-Archimedean local fields, has been established for various reductive groups over the years. However, a construction in full generality was lacking until the recent proposal by Fargues and Scholze, who introduced semi-simplified Langlands parameters for every reductive group. Their construction employs Scholze's theory of diamonds, a modern approach to p-adic analytic geometry. This talk begins by revisiting historical developments in number theory that led to the formulation of the local Langlands correspondence. Subsequently, we explore the relevance of p-adic analytic geometry to the study of the local Langlands program and the impact these innovative methods have on our comprehension of the local Langlands correspondence.
MathQuantum Panel: Industry Careers Applying Math to QIS
When: Thu, December 7, 2023 - 2:00pmWhere: Online
Speaker: Nicolas Delfosse, Hari Krovi, Michelle Lollie, Aaron Lott, Tuhin Sahai (IPST guests) - https://mathquantum.umd.edu
Abstract: RSVP for Zoom link at https://forms.gle/jYUa1v1NPN5VPyQs5
This panel will host 5 researchers working in QIS outside of the academic setting to share about their careers, work, and experiences.
Dr. Nicolas Delfosse is a Principal Researcher working on quantum error correction and fault-tolerant quantum computing. After 6 years at Microsoft, he joined IonQ in December 2023 to lead the work on designing the architecture for a fault-tolerant quantum machine.
Nicolas obtained a PhD degree in Pure Mathematics from the University of Bordeaux, France, under the supervision of Gilles Zémor. Then, he joined Ecole Polytechnique supported by the LIX-Qualcomm fellowship to work with Alain Couvreur. I held a postdoc position at Sherbrooke University in the group of David Poulin and a postdoc position shared between UCR and Caltech in the groups of Leonid Pryadko and John Preskill.
Dr. Hari Krovi works on various aspects of quantum computing and quantum algorithms. He has a PhD from USC and has worked in Raytheon BBN Technologies for several years before recently joining Riverlane (a quantum start-up). At Raytheon, Hari was the lead on several US grants on quantum computing and quantum communications. At Riverlane, he leads a team working on quantum algorithms and analyzing the effect of noise in quantum hardware. He has several publications including ones in high impact journals such as Nature and PNAS. Many of these are results of collaborations with leading institutions such as MIT, the University of Maryland and the University of Sydney.
Dr. Michelle Lollie is an advanced laser scientist at Quantinuum, supporting the design, development, and construction of complex optical systems foundational to building world class quantum computers. She completed her PhD in Physics at Louisiana State University where her research focused on high-dimensional orbital angular momentum states of light for fiber-based quantum cryptography and communication protocols. She participates in various diversity, equity, inclusion, and accessibility initiatives, advocating for those who are marginalized in STEM fields, particularly in physics. Outside of wrangling photons, you can often find her at home practicing the violin.
Dr. Aaron Lott is a senior interdisciplinary scientist and technical area lead in the Research Institute of Advanced Computer Science at USRA. He is a research staff member of the NASA Ames Quantum Artificial Intelligence Laboratory, and an adjunct associate professor at IPST in UMD College Park where he teaches a masters course in quantum computing algorithms and architectures. Aaron earned his Ph.D. in applied mathematics and scientific computation at UMD College Park, and performed post-doctoral research at the NIST and Lawrence Livermore National Laboratory where he worked on scalable solvers for models of fluid flow. Aaron manages USRA’s portfolio of research in collaboration with around 40 USRA scientists & engineers across emerging sensors, machine learning methods and applications and computing architectures, including groups in nanodevices, core data sciences, environmental data science and quantum computing and space life sciences.
Dr. Tuhin Sahai is a Principal Research Scientist at SRI International broadly interested in the verification, optimization, design, and analysis (VODA) of complex interconnected systems in the presence of uncertainty. His projects have spanned the areas of uncertainty quantification, discrete optimization, and quantum computation. He enjoys working at the interface of multiple disciplines and finding common themes and connections. Prior to joining SRI, Dr. Sahai spent 15 years at Raytheon Technologies Research Center (RTRC) where he held positions of increasing responsibility, culminating in the role of a Technical Fellow. He earned his Ph.D. in January 2008 from Cornell University, where he was a McMullen Fellow and won the H.D. Block teaching award. Dr. Sahai received his Master’s and Bachelor’s in Aerospace Engineering from the Indian Institute of Technology, Bombay in 2002.
Single Proxy (Synthetic) Control
When: Mon, December 11, 2023 - 3:30pmWhere: Kirwan Hall 3206
Speaker: Chan Park (University of Pennsylvania) - https://www.chanpark.net/
Abstract: A negative control outcome (NCO) is an outcome that is associated with unobserved confounders of the effect of a treatment on an outcome in view, and is a priori known not to be causally impacted by the treatment. In the first half of the talk, we discuss the single proxy control (SPC) framework, a formal NCO method to detect and correct for residual confounding bias. We establish nonparametric identification of the average causal effect for the treated (ATT) by treating the NCO as an error-prone proxy of the treatment-free potential outcome, a key assumption of the SPC framework. We characterize the efficient influence function for the ATT under a semiparametric model in which nuisance functions are a priori unrestricted. Moreover, we develop a consistent, asymptotically linear, and locally semiparametric efficient estimator of the ATT using modern machine learning theory.
Shifting to the second half of the talk, we introduce the single proxy synthetic control (SPSC) framework, an extension of the SPC framework designed for a synthetic control setting, where a single unit is treated and pre- and post-treatment time series data are available on the treated unit and a heterogeneous pool of untreated control units. Similar to SPC, the SPSC framework views the outcomes of untreated control units as proxies of the treatment-free potential outcome of the treated unit, a perspective we formally leverage to construct a valid synthetic control. Under this framework, we establish alternative identification and estimation methodology for synthetic controls and, in turn, for the ATT. Additionally, we adapt a conformal inference approach to perform inference on the treatment effect, obviating the need for a large number of post-treatment data. We illustrate the SPC and SPSC approaches with real-world applications from the Zika virus outbreak in Brazil and the 1907 financial crisis.
A Data Assimilation System for Lake Erie Based on the Ensemble Transform Kalman Filter (Ph.D. Final Oral Exam)
When: Thu, January 4, 2024 - 1:00pmWhere: MTH 1310
Speaker: David Russell (AMSC) -
Symmetry-Preserving Machine Learning: Theory and Applications
When: Tue, January 23, 2024 - 3:00pmWhere: Kirwan Hall 3206
Speaker: Wei Zhu (University of Massachusetts, Amherst ) - https://www.umass.edu/mathematics-statistics/directory/faculty/wei-zhu
Abstract: Abstract: Symmetry is prevalent in a variety of machine learning (ML) and scientific computing tasks, including computer vision and computational modeling of physical and engineering systems. Empirical studies have demonstrated that ML models designed to integrate the intrinsic symmetry of their tasks often exhibit substantially improved performance. Despite extensive theoretical and engineering advancements in the domain of "symmetry-preserving ML", several critical questions remain unaddressed, presenting unique challenges and opportunities for applied mathematicians.
Firstly, real-world symmetries rarely manifest perfectly and are typically subject to various deformations. Therefore, a pivotal question arises: Can we effectively quantify and enhance the robustness of models to maintain an “approximate" symmetry, even under imperfect symmetry transformations? Secondly, although empirical evidence suggests that symmetry-preserving ML models typically require fewer training data to achieve equivalent accuracy, there is a need for more precise and rigorous quantification of this reduction in sample complexity attributable to symmetry preservation. Lastly, considering the non-convex nature of optimization in modern ML, can we ascertain whether algorithms like gradient descent can guide symmetry-preserving models to indeed converge to objectively better solutions compared to their generic counterparts, and if so, to what degree?
In this talk, I will present several of my research projects addressing these intriguing questions. Surprisingly, the answers are not as straightforward as one might assume and, in some cases, are counterintuitive. If time permits, I will also discuss our recent efforts on extending these results to ML-assisted structure-preserving computational models for complex physical systems.
Cohomology of Arithmetic Groups, Higher Property T and Spectral Gap
When: Mon, January 29, 2024 - 3:15pmWhere: Kirwan Hall 3206
Speaker: Uri Bader (Weizmann Institute of Science)
Abstract:
Groups of matrices with integer entries, aka arithmetic groups, are prominent objects of mathematics. From a geometric point of view, they appear as the fundamental groups of locally symmetric spaces. Topological invariants of such spaces could be seen as group invariants and vice versa. In my talk I will relate this useful link between topology and arithmetics with the theory of unitary representations. More precisely, I will focus on the cohomology of arithmetic groups with unitary coefficients, presenting a recent joint work with Roman Sauer which completely clarifies the theory in small degrees. By the end of the talk I will discuss the relation of the above with the phenomenon of spectral gap and state various related conjectures. I will make an effort to present the subject to a general audience.
Random Packings and Liquid Crystals
When: Fri, February 2, 2024 - 11:00amWhere: Kirwan Hall 3206
Speaker: Ron Peled (Tel Aviv University) - http://www.math.tau.ac.il/~peledron/
Abstract: Let T be a subset of R^d, such as a ball, a cube or a cylinder, and consider all possibilities for packing translates of T, perhaps with its rotations, in some bounded domain in R^d. What does a typical packing of this sort look like? One mathematical formalization of this question is to fix the density of the packing and sample uniformly among all possible packings with this density. Discrete versions of the question may be formulated on lattice graphs.
The question arises naturally in the sciences, where T may be thought of as a molecule and its packing is related to the spatial arrangement of molecules of a material under given conditions. In some cases, the material forms a liquid crystal - states of matter which are, in a sense, between liquids and crystals.
I will give a gentle review of ideas from this topic (with many pictures!), mentioning some of the predictions and the mathematical progress. I will then elaborate on a recent result, joint with Daniel Hadas, on the structure of high-density packings of 2x2 squares with centers on the square lattice.
Continuous bubbling for the harmonic map heat flow
When: Mon, February 5, 2024 - 3:00pmWhere: Kirwan Hall 3206
Speaker: Andrew Lawrie (MIT) - https://math.mit.edu/~alawrie/
Abstract: I will discuss joint work with Jacek Jendrej and Wilhelm Schlag about the two dimensional harmonic map heat flow for maps taking values in the sphere. It has been known since the 80s-90’s that solutions can exhibit bubbling along a well-chosen sequence of times — the solution decouples into a superposition of well-separated harmonic maps and a body map accounting for the rest of the energy. We prove that every sequence of times contains a subsequence along which such bubbling occurs. This is deduced as a corollary of our main theorem, which shows that the solution approaches the family of multi-bubbles in continuous time. The proof is partly motivated by the classical theory of dynamical systems and uses the notion of “minimal collision energy” developed in joint work with Jendrej on the Soliton Resolution Conjecture for nonlinear waves.
Mean curvature flow in spaces with positive cosmological constant
When: Thu, February 15, 2024 - 3:30pmWhere: Kirwan Hall 3206
Speaker: Or Hershkovits ( (Hebrew University)) -
Abstract: Abstract: In this talk, I will describe an approach of using Lorentzian mean curvature flow (MCF) to probe "expanding universes" (such as, presumably, ours) with matter that is assumed to be attracted to matter (formally, this assumption is called the "strong energy condition")
Assuming 2-dimensional symmetry, I will explain how the mean curvature flow can be used to show that such universes become asymptotic, in some sense, to the maximally symmetric such universe - de Sitter space. This proves a special case of the de Sitter no hair conjecture of Hawking and Gibbons.
Unfortunately, the early universe did not support such two-dimensional symmetry, rendering the above mentioned result physically insignificant. As a first step for removing the above symmetry assumption, I will illustrate a condition, natural in the above context, such that any local graphical mean curvature flow (without symmetry) in de Sitter space satisfying that condition converges to a certain "universal flow".
Effort will be made to make the talk accessible to the wide mathematical audience. In particular, no "physics reasoning" will be involved. This is based on a joint work with Creminelli, Senatore and Vasy, and on a joint work with Senatore.
Stable dynamics in incompressible fluids
When: Mon, February 19, 2024 - 3:00pmWhere: Kirwan Hall 3206
Speaker: Michele Coti Zelati (Imperial College, London) - https://www.imperial.ac.uk/people/m.coti-zelati
Abstract: We study the longtime dynamics in incompressible fluids as a consequence of three fundamental stabilization mechanisms: dissipation, mixing, and dispersion. Although in general one may expect stability to arise from a combination of such mechanisms, their distinct nature makes it difficult to treat them in a combined fashion, and the quantitative analysis often (and necessarily) relies on rather different tools. The goal of this talk is to exhibit an approach that overcomes this difficulty in the Boussinesq equations, a classical model describing the evolution of incompressible and stratified flows. This talk is based on joint work with Augusto Del Zotto and Klaus Widmayer.
Algebraic and Differential Geometry A Two-sided Relationship
When: Wed, April 10, 2024 - 3:15pmWhere: Kirwan Hall 3206
Speaker: Nigel Hitchin (Oxford) -
Abstract: Riemannian geometry has long been applied to algebraic varieties but the influence also runs in the opposite direction with algebraic constructions leading to integrable systems, geodesics and solutions to Einstein's equations. The lectures will address different aspects of these, in particular with reference to the moduli spaces which have appeared in geometery since the introduction of gauge theories.
Algebraic and Differential Geometry A Two-sided Relationship
When: Fri, April 12, 2024 - 3:15pmWhere: Kirwan Hall 3206
Speaker: Nigel Hitchin (Oxford) -
Abstract: Riemannian geometry has long been applied to algebraic varieties but the influence also runs in the opposite direction with algebraic constructions leading to integrable systems, geodesics and solutions to Einstein's equations. The lectures will address different aspects of these, in particular with reference to the moduli spaces which have appeared in geometry since the introduction of gauge theories.
The Mathematics of Doodling (Kirwan Undergraduate Lecture)
When: Tue, April 16, 2024 - 4:00pmWhere: Kirwan Hall 3206
Speaker: Ravi Vakil (Stanford University) - http://math.stanford.edu/~vakil/
Abstract: Doodling is a creative and fundamentally human activity, resulting in doodles with intricate and often hidden implicit structure. We will treat doodles as an example for how mathematics is done — by starting with some doodles, we will ask ourselves some natural questions and see where they take us. They will lead us to some unexpected places, and to some sophisticated mathematics.
Long Time Dynamics of Fluids and Plasmas
When: Wed, April 17, 2024 - 3:15pmWhere: Kirwan Hall 3206
Speaker: Peter Constantin (Princeton University) - https://web.math.princeton.edu/~const/
(Topics course) Digital models, scientific machine learning, and digital twins: a virtuous interplay between data-driven algorithms and physics-inspired numerical models
When: Wed, April 24, 2024 - 12:00pmWhere: Kirwan Hall 3206
Speaker: Alfio Quarteroni (Polytechnic University of Milan) - https://mox.polimi.it/people/alfio-quarteroni/
Abstract: Problem setting is a critical precursor to problem solving. It involves the art of formulating the right problem statement. The importance of this phase is underscored by the fact that without a well-defined problem, finding the right tools and techniques for problem solution becomes a cumbersome and often futile endeavor. This transition from problem setting to problem solving is integral to the larger paradigm of knowledge development. While AI tools have made tremendous strides in recent years, they remain dependent on the foundation laid by human intelligence. Mathematicians, with their ability to discern patterns and relationships, data, and variables, play a vital role in this stage. In this course, I will introduce basic mathematical concepts from both traditional machine learning and scientific machine learning. Scientific machine learning, which integrates data-driven machine learning algorithms with physics-based digital models, provides an ideal platform for the virtuous merging of problem setting and problem solving, facilitated by a profound domain knowledge.
During the course, the reference application will focus on the development of a mathematical simulator for the cardiac function.