#### Research

A mission statement would be nice here (look at Talks, Teaching, Outreach, where I already wrote something more contentful)-

What drives you in your research. Maybe starting with what you like about mathematics in general and then moving to certain areas that are of special interest to you. How you got started with those puzzles.... whatever... (very short - if possible not longer than this dummy text)

Also some remarks about in how far you are also interested in possible applications of your research. And that research is quite a collaborative thing...

### May 2018

#### Current Research Projects

### H. Alpert, É. Roldán

### Art Gallery Problem with Rook and Queen Vision

Summary. We give a complete solution to the extremal topological combinatorialproblem of finding the minimum number of tiles needed to construct a poly-omino withhholes. We denote this number byg(h)and say that a poly-omino is crystallized if it hashholes andg(h)tiles. We analyze structuralproperties of crystallized polyominoes and characterize their efficiency bya topological isoperimetric inequality that relates minimum perimeter, thearea of the holes, and the structure of the dual graph of a polyomino. Wealso develop a new dynamical method of creating sequences ofpolyomi-noes which is invariant with respect to crystallization andefficient structure.

### H. Alpert, É. Roldán

### Art Gallery Problem with Rook and Queen Vision

Summary. We give a complete solution to the extremal topological combinatorialproblem of finding the minimum number of tiles needed to construct a poly-omino withhholes. We denote this number byg(h)and say that a poly-omino is crystallized if it hashholes andg(h)tiles. We analyze structuralproperties of crystallized polyominoes and characterize their efficiency bya topological isoperimetric inequality that relates minimum perimeter, thearea of the holes, and the structure of the dual graph of a polyomino. Wealso develop a new dynamical method of creating sequences ofpolyomi-noes which is invariant with respect to crystallization andefficient structure.

### H. Alpert, É. Roldán

### Art Gallery Problem with Rook and Queen Vision

Summary. We give a complete solution to the extremal topological combinatorialproblem of finding the minimum number of tiles needed to construct a poly-omino withhholes. We denote this number byg(h)and say that a poly-omino is crystallized if it hashholes andg(h)tiles. We analyze structuralproperties of crystallized polyominoes and characterize their efficiency bya topological isoperimetric inequality that relates minimum perimeter, thearea of the holes, and the structure of the dual graph of a polyomino. Wealso develop a new dynamical method of creating sequences ofpolyomi-noes which is invariant with respect to crystallization andefficient structure.

#### Research Highlights

### H. Alpert, É. Roldán

### Art Gallery Problem with Rook and Queen Vision

Abstract. Click here to add your own text and edit me. It’s easy. Just click “Edit Text” or double click me to add your own content and make changes to the font. Just click “Edit Text” or double click me to add your own content and make changes to the font. Just click “Edit Text” or double click me to add your own content and make changes to the font. Just click “Edit Text” or double click me to add your own content and make changes to the font. Just click “Edit Text” or double click me to add your own content and make changes to the font.

### H. Alpert, É. Roldán

### Art Gallery Problem with Rook and Queen Vision

Abstract. Click here to add your own text and edit me. It’s easy. Just click “Edit Text” or double click me to add your own content and make changes to the font. Just click “Edit Text” or double click me to add your own content and make changes to the font. Just click “Edit Text” or double click me to add your own content and make changes to the font. Just click “Edit Text” or double click me to add your own content and make changes to the font. Just click “Edit Text” or double click me to add your own content and make changes to the font.

### H. Alpert, É. Roldán

### Art Gallery Problem with Rook and Queen Vision

Abstract. Click here to add your own text and edit me. It’s easy. Just click “Edit Text” or double click me to add your own content and make changes to the font. Just click “Edit Text” or double click me to add your own content and make changes to the font. Just click “Edit Text” or double click me to add your own content and make changes to the font. Just click “Edit Text” or double click me to add your own content and make changes to the font. Just click “Edit Text” or double click me to add your own content and make changes to the font.