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<h1></h1>
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<div class="homepage-content text-justify"><img hspace="10" align=right src="/mb_photo_lanc_small.jpg" width="220">
<h1 id="maciej-buze">Maciej Buze</h1>
<h3> Assistant Professor (Lecturer)<br> in Mathematics and AI
<h4>
MARS: Mathematics for AI in Real-world Systems
<br> School Of Mathematical Sciences
<br> Lancaster University
<br> Lancaster LA1 4YW
<br> United Kingdom
</h4>
<p>Office: S&T Building B004a
<br>
(departmental website link to be added)</a>
<br>
<br>
Email: m[dot]buze[at]lancaster[dot]ac[uk]</p>
<p><b><span style="font-size:1.4em;">Research interests:</span></b><br></p>
<p>My research spans a wide range of topics at the intersection of
<strong>applied and computational mathematics</strong> and <strong>mathematical analysis</strong>
and is primarily inspired by <strong>applications in materials science, biology, physics and data science</strong>.</p>
<p>I use and develop tools in <strong>calculus of variations, bifurcation theory, numerical analysis, optimal transport, uncertainty quantification, approximation theory, scientific GPU computing, data analysis</strong> and <strong>machine learning</strong>.</p>
<p>Current applications include atomistic modelling of defects in crystalline materials, bottom-up upscaling approaches to the modelling of near-crack-tip plasticity, geometric modelling of microstructure in polycrystalline materials (with <strong>industrial partner, Tata Steel</strong>), quantifying uncertainties when modelling materials with interatomic potentials, image processing and generation; barycentric data compression.</p>
<p>I currently have three major ongoing research projects (see <a href="research">Research tab</a> for details):</p>
<ul>
<li><strong>Discrete modelling of nucleation and migration of defects in materials</strong></li>
<li><strong>Optimal transport: theory and applications</strong></li>
<li><strong>Uncertainty quantification for machine learning interatomic potentials</strong></li>
</ul>
<br>
<p><b><span style="font-size:1.4em;">PhD opportunities:</span></b></p>
<p>MARS is offering 4-year fully-funded PhD studentships. I will be supervising two projects:</p>
<ul>
<li><a href="https://www.lancaster.ac.uk/maths/research/mars/phds/mars-indicative-phd-projects/#numerical-continuation-and-deflation-techniques-for-atomistic-modelling-of-materials-605030-1">Numerical continuation and deflation techniques for atomistic modelling of materials</a></li>
<li><a href="https://www.lancaster.ac.uk/maths/research/mars/phds/mars-indicative-phd-projects/#minimisation-diagrams-optimal-transport-and-logistic-regression-with-applications-to-microstructure-modelling-in-metals--605030-2"> Minimisation diagrams, optimal transport and logistic regression, with applications to microstructure modelling in metals.</a></li>
</ul>
<p>Please get in touch if you are interested!<br></p>
<!-- I use and develop tools in <u>calculus of variations</u>, <u>bifurcation theory</u>, <u>numerical analysis</u>, <u>optimal transport</u>, <u>uncertainty
quantification</u>, <u>approximation theory</u>, and <u>scientific GPU computing</u>. Current applications include atomistic modelling of defects in crystalline materials, bottom-up approaches to the modelling of near-crack-tip plasticity, geometric modelling of microstructure in polycrystalline materials (with <b>industrial partner, Tata Steel</b>), and quantifying uncertainties when modelling materials with interatomic potentials. Specific topics include (see <a href="research">Research tab</a> for details):
<br>
<b>Mathematical aspects of materials science:</b>
- atomistic modelling of fracture and other crystal defects,
- bottom-up approaches to near-crack-tip plasticity,
- bottom-up approaches to grain boundaries,
- geometric modelling of polycrystaline materials,
- defect nucleation and propagation as a bifurcation phenomenon,
- uncertainty quantification for interatomic potentials.
<br>
<b>Optimal transportation theory:</b>
- various aspects of unbalanced optimal transport: entropic regularisation, generalised lifting theory, computation of barycenters
- anisotropic power diagrams: GPU-accelerated efficient computation via (semi-) discrete optimal transport, with applications to polycrystalline modelling. -->
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<p class="copyright text-muted">© 2024 Maciej Buze; All rights reserved. Powered by <a href="https://gohugo.io">Hugo</a>, <a href="https://github.com/calintat/minimal">Minimal</a> and <a href="https://katex.org/">KaTeX</a>.</p>
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